Math Problem Library

1)  Which of the following is NOT TRUE about the distribution for averages?
a. The mean, median, and mode are equal.
b. The area under the curve is one.
c. The curve never touches the x-axis.
d. The curve is skewed to the right.

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2)  A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 85 and 125 points?

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3)  Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______)
b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80th percentile of the distribution of the average of 49 fly balls

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4)  Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site. On average, 28 percent of 18 to 34 year olds check their Facebook profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a standard deviation of five percent.
a. Find the probability that the percent of 18 to 34-year-olds who check Facebook before getting out of bed in the morning is at least 30.
b. Find the 95th percentile, and express it in a sentence.

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5)  Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.
a. If X = distance in feet for a fly ball, then X ~
b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.

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6)  Height and weight are two measurements used to track a child's development. TheWorld Health Organization measures child development by comparing the weights of children who are the same height and the same gender. In 2009, weights for all 80 cm girls in the reference population had a mean μ = 10.2 kg and standard deviation σ = 0.8 kg. Weights are normally distributed. X ~ N(10.2, 0.8). Calculate the z-scores that correspond to the following weights and interpret them.
a. 11 kg
b. 7.9 kg
c. 12.2 kg

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8)  The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.
What is the median recovery time?
a. 2.7
b. 5.3
c. 7.4
d. 2.1

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9)  Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph. a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?
b. What proportion of the vehicles would be going less than 50 mph?
c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?
d. In what way do you think the actual distribution of speeds differs from a normal distribution?

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10)  A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4.
(a) Everyone who scores in the top 30% of the distribution gets a certificate.
(b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state?

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11)  The singular form of the word "dice" is "die". Tom was throwing a six-sided die. The first time he threw, he got a three; the second time he threw, he got a three again. What's the probability of getting a three at the third time?

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12)  Jennie and Alex both wanted to get a free ticket for a College Music concert. However, the concert staff told them the tickets were limited. Twenty people wanted to attend the concert but only 10 free tickets were left. So the concert center staff decided to use a lottery to decide who would receive the free tickets. What's the probability of Jennie and Alex both getting free tickets?

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13)  If you throw a die for two times, what is the probability that you will get a one on the first throw or a one on the second throw (or both)?

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14)  A toy factory makes 5,000 teddy bears per day. The supervisor randomly selects 10 teddy bears from all 5,000 teddy bears and uses this sample to estimate the mean weight of teddy bears and the sample standard deviation. How many degrees of freedom are there in the estimate of the standard deviation?

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15)  Imagine that the diabetic test accurately indicates the disease in 95% of the people who have it. What's the miss rate?

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16)  Which of the following is the probability that subjects do not have the disease, but the test result is positive?
a. Miss rate
b. False positive rate
c. Base rate
d. Disease rate

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17)  You choose an alpha level of .01 and then analyze your data.
(a) What is the probability that you will make a Type I error given that the null hypothesis is true?
(b) What is the probability that you will make a Type I error given that the null hypothesis is false.

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18)  Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects getting better each trial? Test the linear effect of trial for the data.
A score trial 1B score trial 2C Score trial 3
467
378
285
147
469
242

(a) Compute L for each subject using the contrast weights -1, 0, and 1. That is, compute (-1)(a) + (0)(b) + (1)(c) for each subject.
(b) Compute a one-sample t-test on this column (with the L values for each subject) you created. Formula t = To computer a one-sample t-test first know the meaning of each letter

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19)  Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the Type I error is:
a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher
b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same
c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher
d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher

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20)  Cole and Finn are roommates. They paid three months' rent and a $200 security deposit when they signed the lease. In total, they paid $1,850. What is the rent for one month? Write an equation and solve it.

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21)  Given that P (A)=0.6, P (B)=0.5, P (A|B) = 0.2, P (C|A)= 0.3 and P (C|B)=0.4.
(1) If they are dependent each other, what is P (A ? B) = ?
(2) If the event C is conditionally dependent upon evens A and B, What's the probability: P (A|C) = ?

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22)  Of all smokers in particular district, 40% prefer brand A and 60% prefer brand B. Of those who prefer brand A, 30% are female, and of those who prefer brand B, 40% are female.
Q: What is the probability that a randomly selected smoker prefers brand A, given that the person selected is a female?

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24)  Consider a firm that has two assembly lines, 1 and 2, both producing calculator. Assume that you have purchased a calculator and it turns out to be defective. And the line 1 produces 60% of all calculators produced.
L1: event that the calculator is produced on line 1
L2: event that the calculator is produced on line 2
Suppose that your are given the conditional information: 10% of the calculator produced on line 1 is defective 20% of the calculator produced on line 2 is defective
Q: If we choose one defective, what is the probability that the defective calculator comes from Line 1 and Line2?

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25)  Consider the case of a manufacturer who has an automatic machine that produces an important part. Past records indicate that at the beginning of the data the machine is set up correctly 70 percent of the time. Past experience also shows that if the machine is set up correctly it will produce good parts 90 percent of the time. If it is set up incorrectly, it will produce good parts 40 percent of the time. Since the machine will produce 60 percent bad parts, the manufacturer is considering using a testing procedure. If the machine is set up and produces a good part, what is the revised probability that it is set up correctly?

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26)  Eighty percent of the employees at Rowan University have their biweekly Wages deposit directly to their bank by electronic deposit program. Suppose we select a random samples of 8 employees. What is the probability that three of the eight (8) sampled employees use direct deposit program?

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27)  Suppose that previously collected traffic data indicate that, during the afternoon rush hour, an average of 4 cars arrive at a toll bridge each second. If it is assumed that cars arrive randomly, and can thus be modeled with Poisson distribution, what is the probability that in the next second, NO cars will arrive?

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28)  Customers arrive at the claims counter at the rate of 20 per hour (Poisson distributed). What is the probability that the arrival time between consecutive customers is less than five minutes?

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29)  An analysis of the final test scores for Managerial Decision Making Tools reveals the scores follow the normal probability distribution. The mean of the distribution is 75 and the standard deviation is 8. The instructor wants to award an "A" to students whose score is in the highest 10 percent. What is the dividing point for those students who earn an "A"?

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30)  It is estimated that weekly demand for gasoline at new station is normally distributed, with an average of 1,000 and standard deviation of 50 gallons. The station will be supplied with gasoline once a week. What must the capacity of its tank be if the probability that its supply will be exhausted in a week is to be no more than 0.01?

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32)  A financial analyst computed the ROI for all companies listed on the NYSE. She found that the mean of this distribution was 10% with standard deviation of 5%. She is interested in examining further those companies whose ROI is between 14% and 16% of the approximately 1,500 companies listed on the exchange, how many are of interest of her?

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33)  The hourly wages of employees at Rowan have a mean wage rate of $10 per hour with a standard deviation of $1.20. What is the probability the mean hourly wage of a random sample of 36 employees will be larger than $10.50? Assume the company has a total of 1,000 employees

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34)  A candidate for mayor wants to gauge potential voter reaction to an increase recreational services by estimating the proportion of voter who now use city services. If we assume that 50% of the voters require city recreational services, what is the probability that 40% or fewer voters in a sample of 100 actually will use these city services?

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35)  Suppose that the manager of the Commerce Bank at Glassboro determines that 40% of all depositors have a multiple accounts at the bank. If you, as a branch manager, select a random sample of 200 depositors, what is the probability that the sample proportion of depositors with multiple accounts is between 35% and 50%?

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36)  A random sample of 144 with a mean of 100 and a standard deviation of 70 is known from a population of 1,000. What is the 95% confidence interval for the unknown population

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37)  A random sample of n = 10 flash light batteries with a mean operating life X=5 hr. And a sample standard deviation S = 1 hr. is picked from a production line known to produce batteries with normally distributed operating lives. What's the 98% confidence interval for the unknown mean of the working life of the entire population of batteries?

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38)  The NJ state education department finds that in a random sample of 100 persons who attended college, 40 received a college degree. What's the 95% confidence interval for the proportion of college graduates out of all the persons who attended college?

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39)  Suppose a firm producing light bulbs wants to know if it can claim that its light bulbs it produces last 1,000 burning hours (μ). To do this, the firm takes a random sample of 100 bulbs and find its average life time (X=980 hrs) and the sample standard deviation s = 80 hrs. If the firm wants to conduct the test at the 1% of significance, what's you final suggestion? (i..e, Should the producer accept the Ho that its light bulbs have a 1,000 burning hrs. at the 1% level of significance?) Ho: μ = 1,000 hours. Ha: μ ≠ 1,000 hours.

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40)  A firm wants to know with a 98% level of confidence if it can claim that the boxes of detergent it sells contain more than 500g of detergent. From past experience the firm knows that the amount of detergent in the boxes is normally distributed. The firm takes a random sample of n =25 and finds that X = 520 g and s = 75g. What's your final conclusion? (4 pts.)
(Ho: μ = 500; Ha: μ > 500)

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41)  A Government antipollution spokeperson asserts that more than 80% of the plants in the Glassboro area meet the antipollution standards. An antipollution advocate does not believe the government claim. She takes a random sample of published data on pollution emission for 64 plants in the area and finds that 56 plants meet the pollution standards. Do the sample data support the government claim at the 1% level of significance? (3 pts.)
(H0: ρ=0.8; Ha: ρ>0.8)

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42)  A researcher believed that there was a difference in the amount of time boys and girls at 7th grade studied by using a two-tailed t test. Which of the following is the null hypothesis?
a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per day
b. Mean of hours that boys studied per day was greater than mean of hours that girls studied per day
c. Mean of hours that boys studied per day was smaller than mean of hours that girls studied per day
d. Mean of hours that boys studied per day was smaller than or equal to mean of hours that girls studied per day

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43)  A professor assumed there was a correlation between the amount of hours people were expose to sunlight and their blood vitamin D level. The null hypothesis was that the population correlation was__
a. Positive 1.0
b. Negative 1.0
c. Zero
d. Positive 0.50

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44)  Conventionally, the null hypothesis is false if the probability value is:
a. Greater than 0.05
b. Less than 0.05
c. Greater than 0.95
d. Less than 0.95

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45)  A teacher hypothesized that in her class, grades of girls on a chemistry test were the same as grades of boys. If the probability value of her null hypothesis was 0.56, it suggested:
a. We failed to reject the null hypothesis
b. Boys' grades were higher than girls' grades
c. Girls' grades were higher than boys' grades
d. The null hypothesis was rejected

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46)  Which of the following could reduce the rate of Type I error?
a. Making the significant level from 0.01 to 0.05
b. Making the significant level from 0.05 to 0.01
c. Increase the Β level
d. Increase the power

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47)  ___is the probability of a Type II error; and ___ is the probability of correctly rejecting a false null hypothesis.
a. 1 - Β; Β
b. Β; 1 - Β
c. α; Β
d. Β; α

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48)  A student hypothesized that girls in his class had the same blood pressure levels as boys. The probability value for his null hypothesis was 0.15. So he concluded that the blood pressures of the girls were higher than boys'. Which kind of mistake did he make?
a. Type I error
b. Type II error
c. Type I and Type II error
d. He did not make any mistake

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49)  When you conduct a hypothesis testing, at which of the following P-value, you feel more confident to reject the null hypothesis?
a. 0.05
b. 0.01
c. 0.95
d. 0.03

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50)  A student posed a null hypothesis that during the month of September, the mean daily temperature of Boston was the same as the mean daily temperature of New York. His alternative hypothesis was that mean temperatures in these two cities were different. He found the P value of his null hypothesis was 0.56. Thus, he could conclude:
a. In September, Boston was colder than New York
b. In September, Boston was warmer than New York
c. He may reject the null hypothesis
d. He failed to reject the null hypothesis

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51)  If the P-value of a hypothesis test is 0.40, you conclude
a. You accept the null hypothesis
b. You reject the null hypothesis
c. You failed to reject the null hypothesis
d. You think there is a significant difference

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52)  A teacher assumed that the average of grades for a math test was 80. Imagine 20 students took the test and the 95% confidence interval of grades was (83, 90). Can you reject the teacher's assumption?
a. Yes
b. No
c. We cannot tell from the given information

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53)  Which of the following descriptions of confidence interval is correct? (Select all that apply)
a. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0
b. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0
c. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1
d. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1

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54)  If a statistical test result is not significant at the 0.05 level, then we can conclude:
a. It is not significant at 0.01 level
b. It is not significant at 0.10 level
c. It must be significant at 0.01 level
d. It must be significant above 0.05 level

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55)  Power is equal to:
a. α
b. Β
c. 1 - α
d. 1 - Β

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56)  Which of the following descriptions of null hypothesis are correct? (Select all that apply)
a. A null hypothesis is a hypothesis tested in significance testing.
b. The parameter of a null hypothesis is commonly 0.
c. The aim of all research is to prove the null hypothesis is true
d. Researchers can reject the null hypothesis if the P-value is above 0.05

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57)  Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What's the sample standard deviation?

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58)  Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What's the standard error of the mean?

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59)  Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. The researcher posed a null hypothesis that the average weight for boys in that high school should be 100 lbs. What is the absolute value of calculated t that we use for testing the null hypothesis?

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60)  Imagine a researcher posed a null hypothesis that in a certain community, the average energy expenditure should be 2,100 calories per day. He randomly sampled 100 people in that community. After he computed the t value by calculating a two-tailed t-statistic, he found that the probability value was 0.10. Thus, he concluded:
a. The average energy expenditure was bigger than 2,100 calories per day
b. The average energy expenditure was smaller than 2,100 calories per day
c. He could not reject the null hypothesis that the average energy expenditure was 2,100 calories per day
d. The average energy expenditure was either more than 2,100 calories per day or less than 2,100 calories per day

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61)  Compared to the normal distribution, the t distribution has ___ values at the top and ___ at the tails.
a. More; less
b. More; more
c. Less; less
d. Less; more

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62)  In order to test if there is a difference between means from two populations, which of following assumptions are NOT required?
a. The dependent variable scores must be a continuous quantitative variable.
b. The scores in the populations are normally distributed.
c. Each value is sampled independently from each other value.
d. The two populations have similar means

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63)  A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 120 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 6.0. What's the absolute value of the difference between means?

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64)  A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What is the standard error of the difference in means?

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65)  A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What's the t-value (two-tailed) for the null hypothesis that boys and girls have the same test scores?

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66)  Which of the following involves making pairwise comparisons?
a. Comparing the standard deviation of GRE grades between two states
b. Comparing the variance of the amount of soda consumed by boys and girls in a high school
c. Comparing the mean weight between children in grades 2, 3, 4 and 5
d. Comparing the number of restaurants in New York and Boston

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67)  A professor wanted to test all possible pairwise comparisons among six means. How many comparisons did he need to compare?
a. 5
b. 6
c. 10
d. 15

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68)  A professor wants to test all possible pairwise comparisons among three means. If we need to maintain an experiment-wise alpha of 0.05, what is the error rate per comparison after applying Bonferroni correction?

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69)  Which of the followings can increase the value of t? (select all the apply)
a. Increase the standard deviation of difference scores
b. Decrease the standard deviation of difference scores
c. Increase the difference between means
d. Decrease the difference between means

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70)  Imagine a researcher wanted to test the effect of the new drug on reducing blood pressure. In this study, there were 50 participants. The researcher measured the participants' blood pressure before and after the drug intake. If we want to compare the mean blood pressure from the two time periods with a two-tailed t test, how many degrees of freedom are there?
a. 49
b. 50
c. 99
d. 100

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71)  Which of the followings is the definition of power?
a. Power is the probability of rejecting a null hypothesis
b. Power is the probability of accepting a null hypothesis
c. Power is the probability of accepting a false null hypothesis
d. Power is the probability of rejecting a false null hypothesis

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72)  The probability of failing to reject a false null hypothesis is ____
a. α
b. 1 - α
c. 1 - Β
d. Β

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73)  If power is big, you can assume:
a. The difference between the means is more likely to be detected
b. The significance level set by the researcher must be high
c. We increase the probability of type I error
d. Your study result will be more likely to be inconclusive

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74)  If the probability that you will correctly reject a false null hypothesis is 0.80 at 0.05 significance level. Therefore, α is__ and Β is__.

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75)  As the sample size increases, we assume:
a. α increases
b. Β increases
c. The probability of rejecting a hypothesis increases
d. Power increases

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76)  Which of the following can increase power?
a. Increasing standard deviation
b. Decreasing standard deviation
c. Increasing both means but keeping the difference between the means constant
d. Increasing both means but making the difference between the means smaller

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77)  Can a coefficient of determination be negative? Why or why not?

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78)  Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.
(a) The number of customers arriving at a bank between noon and 1:00 P.M.
(i) The random variable is continuous. The possible values are x ≥ 0.
(ii) The random variable is discrete. The possible values are x = 0, 1, 2,...
(iii) The random variable is continuous. The possible values are x = 0, 1, 2,...
(iv) The random variable is discrete. The possible values are x ≥ 0.

(b) The amount of snowfall
(i) The random variable is continuous. The possible values are s = 0, 1, 2,...
(ii) The random variable is discrete. The possible values are s ≥ 0.
(iii) The random variable is discrete. The possible values are s = 0, 1, 2,...
(iv) The random variable is continuous. The possible values are s ≥ 0.

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79)  A binomial probability experient is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 40, p = 0.05, x = 2
P(2) =

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80)  Determine the area under the standard normal curve that lies between:
(a) Z = -0.38 and Z = 0.38
(b) Z = -2.66 and Z = 0
(C) Z = -1.04 and Z - 1.67

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81)  Determine μx and σx from the given parameters of the population and sample size
μ = 76, σ = 28, n = 49
μx = ?
σx = ?

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82)  Construct a confidence interval of the population proportion at the given level of confidence.
x = 120, n = 300, 99% confidence
Round to 3 decimal places as needed

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83)  Six Years ago, 12.2% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then.
(a) Which of the following is the hypothesis to be conducted?
A. H0: p = 0.122, H1 p > 0.122
B. H0: p = 0.122, H1 p ≠ 0.122
C. H0: p = 0.122, H1 p < 0.122

(b) Which of the following is a Type I error?
A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage.

c) Which of the following is a Type II error?
A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage
B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage
C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%


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84)  A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.22 hours, with a standard deviation of 2.31 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.29 hours, with a standard deviation of 1.58 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children (μ1 - μ2)
What is the interpretation of this confidence interval?
A. There is 90% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours
B. There is a 90% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours
C. There is 90% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours
D. There is a 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours


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85)  The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 231 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer.
DigitProbability
10.301
20.176
30.125
40.097
50.079
60.067
70.058
80.051
90.046
Fradulent Checks
DigitFrequency
136
232
345
420
524
636
715
816
97

Complete parts (a) and (b).
(a) Using the level of significance α = 0.05, test whether the first digits in the allegedly fraudulent checks obey Benford's Law. Do the first digits obey the Benford's Law?
Yes or No

Based o the results of part (a), could one think that the employe is guilty of embezzlement?
Yes or No

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86)  Write a model that utilizes all three explanatory variables with no interaction or quadratic terms. Choose the correct answer below.
A. yi = Β0 + Β1x1 + Β2x2 + Β3x3 + εi
B. yi = Β0 + Β1x1 + Β2x2 + Β3x3x2 + εi
C. yi = Β1x1 + Β2x2 + Β3x3 + εi
D. None of the above equations satisfy all of the conditions

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87)  True or False
(a) The normal distribution curve is always symmetric to its mean.
(b) If the variance from a data set is zero, then all the observations in this data set are identical.
(c) P(A AND Ac)=1, where Ac is the complement of A.
(d) In a hypothesis testing, if the p-value is less than the significance level α, we do not have sufficient evidence to reject the null hypothesis.
(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.

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88)  A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes).
Checkout Time (in minutes)FrequencyRelative Frequency
1.0 - 1.92?
2.0 - 2.98?
3.0 - 3.9??
4.0 - 5.95?
Total25?

(a) Complete the frequency table with frequency and relative frequency.
(b) What percentage of the checkout times was less than 3 minutes?
(c)In what class interval must the median lie? Explain your answer.
(d) Assume that the largest observation in this dataset is 5.8. Suppose this observation were incorrectly recorded as 8.5 instead of 5.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Why?

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89)  A random sample of STAT200 weekly study times in hours is as follows: 2 15 15 18 30 Find the sample standard deviation. (Round the answer to two decimal places. Show all work.

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90)  A fair coin is tossed 4 times.
a) How many outcomes are there in the sample space?
b) What is the probability that the third toss is heads, given that the first toss is heads? c) Let A be the event that the first toss is heads, and B be the event that the third toss is heads. Are A and B independent? Why or why not?

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91)  There are 1000 juniors in a college. Among the 1000 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses.

a) What is the probability that a randomly selected junior is taking at least one of these two courses?
b) What is the probability that a randomly selected junior is taking PSYC300, given that he/she is taking STAT200?

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92)  CCP Stat Club is sending a delegate of 2 members to attend the 2015 Joint Statistical Meeting in Seattle. There are 10 qualified candidates. How many different ways can the delegate be selected?

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93)  magine you are in a game show. There are 4 prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and two are worth $10. You have to pay $20 to the host if your choice is not correct. Let the random variable x be the winning

(a) What is your expected winning in this game?
(b) Determine the standard deviation of x. (Round the answer to two decimal places)

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94)  Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent's serves. Assume her opponent serves 8 times. Show all work. Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution.

a) What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?
b) Find the probability that that she returns at least 1 of the 8 serves from her opponent.
(c) How many serves can she expect to return?


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95)  The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

a) What is the probability that a randomly person has an IQ between 85 and 115?
b) Find the 90th percentile of the IQ distribution/
c) If a random sample of 100 people is selected, what is the standard deviation of the sample mean?

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96)  A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime.

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97)  4 people like ketchup, 1 person likes tomato. How many people like ketchup or tomato?

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98)  Rearrange the following equation to make x the subject, and select the correct rearrangement from the list below
3x + 2y
4x + y
=
  
1
3

Select one:
x  =  7y
  13

x  =  7y
  5

x = -7y
x = -3y
x  =  3y
  5

x  =  -5y
  13

x = -y

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99)  A man stands at point p, 45 metres from the base of a building that is 20 metres high.
Find the angle of elevation of the top of the building from the man.

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100)  Suppose that Sn = 3 + 1/3 + 1/9 + ··· + 1/3n - 2
a) Find S10 and S
b) If the common difference in an arithmetic sequence is twice the first term, show that Sn/Sm = n2/m2

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101)  You can afford monthly deposits of $270 into an account that pays 3.0% compounded monthly. How long will it be until you have $11,100 to buy a boat. Round to the next higher month.

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102)  What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.4%? Round to three decimal places. Use a 365 day year.

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103)  If you buy a computer directly from the manufacturer for $3,509 and agree to repay it in 36 equal installments at 1.73% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?PMT =

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104)  You have $250,000 in an IRA (Individual Retirement Account) at the time you retire. You have the option of investing this money in two funds: Fund A pays 5.4% annually and Fund B pays 7.9% annually. How should you divide your money between fund jA and Fund B to produce an annual interest income of $14,750?

You should invest $______in Fund A and $___________in Fund B.

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105)  Find the elements on the principal diagonal of matrix B
 0  0  8 
 -1  3  0 
 2  -5  -7 


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106)  From a standard 52 card deck, how many 6-card hands will have 2 spades and 4 hearts?

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107)  Determine if the statement below is True or False
If B ⊂ A, then A ∩ B = B
Is this statement True or False?

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108)  If 13,754 people voted for a politician in his first election, 15,420 voted for him in his second election, and 8,032 voted for him in the first and second elections, how many people voted for this politician in the first or second election?

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109)  A bag contains 10 red balls, 10 green balls and 6 white balls. Two balls are drawn at random from the bag without replacement. What is the probability that they are of different colours?

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110)  t-shirts sell for $19.97 and cost $14.02 to produce. Which equation represents p, the profit, in terms of x, the number of t-shirts sold?
A) p = $19.97x - $14.02
B) p = x($19.97 - $14.02)
C) p = $19.97 + $14.02x
D) p = x($19.97 + $14.02)

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111)  Jazmin is a hairdresser who rents a station in a salon for daily fee. The amount of money (m) Jazmin makes from any number of haircuts (n) a day is described by the linear function m = 45n - 30
A) A haircut costs $30, and the station rent is $45
B) A haircut costs $45, and the station rent is $30.
C) Jazmin must do 30 haircuts to pay the $45 rental fee.
D) Jazmin deducts $30 from each $45 haircut for the station rent.

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112)  A box contains 22 red apples and 3 green apples. Three apples are selected at random, one after the other, without replacement. please show the steps.
(a) The first two apples are green. What is the probability that the third apple is red?
(b) What is the probability that exactly two of the three apples are red?

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113)  Ms. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngest and the middle son gets $35 more than the youngest, how much does each boy get?

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114)  In simple linear regression the slope and the correlation coefficient will have the same signs
True
False

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115)  The coefficient of determination is found by taking the square root of the coefficient of correlation.
True
False

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116)  If the correlation between two variables is close to minus one, the association is:
Strong
Moderate
Weak
None

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117)  What can we conclude if the coefficient of determination is 0.94?
Strength of relationship is 0.94
Direction of relationship is positive
94% of total variation of one variable(y) is explained by variation in the other variable(x).
All of the above are correct

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118)  What is the range of possible values for a coefficient of correlation?

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119)   Assume that you make random guesses for 5 true-or-false questions.
(a) What is the probability that you get all 5 answers correct? (Show work and write the answer in simplest fraction form)
(b) What is the probability of getting the correct answer in the 5th question, given that the first four answers are all wrong? (Show work and write the answer in simplest fraction form)
(c) If event A is “Getting the correct answer in the 5th question” and event B is “The first four answers are all wrong”. Are event A and event B independent? Please explain.

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120)  A high school with 1000 students offers two foreign language courses : French and Japanese. There are 200 students in the French class roster, and 80 students in the Japanese class roster. We also know that 30 students enroll in both courses. Find the probability that a random selected student takes neither foreign language course.

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121)  Men's heights are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. Mimi is designing a plane with a height that allows 95% of the men to stand straight without bending in the plane. What is the minimum height of the plane?

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122)  True or False: The standard deviation of the chi-square distribution is twice the mean.

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123)  If an experiment is conducted with 5 conditions and 6 subjects in each condition, what are dfn and dfe?

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124)  If you are running 6 miles per hour, then it takes you 10 minutes to run 1 mile. If you are running 8 miles per hour, it takes you 7.5 minutes to run a mile. What does your speed have to be for your speed in miles per hour to be equal to your mile time in minutes?

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125)  Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What could N be? Is there more than one answer?

For example, for 23 P(23) = 6 and S(23) = 5, but 23 could not be the N that we want since 23 ≠ 5 + 6

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126)  A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and walked back to the starting point along the same path. She walks 4mph on level ground, 3 mph uphill, and 6 mph downhill. Find the distance she walked.
Hint: Think about d = rt, which means that t = d/r. Think about each section of her walk, what is the distance and the rate. You know that the total time is 5 hours, so you know the sum of the times from each section must be 5.

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127)  A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over all the containers of eggs. Though she is unhurt, every egg is broken. So she goes to her insurance agent, who asks her how many eggs she had. She says she doesn't know, but she remembers somethings from various ways she tried packing the eggs. When she put the eggs in groups of two, three, four, five, and six there was one egg left over, but when she put them in groups of seven they ended up in complete groups with no eggs left over. What can the farmer figure from this information about the number of eggs she had? Is there more than one answer?

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128)  Jack and Jill have a magic pail of beans. The number of beans in the pail doubles every second. If the pail is full after 10 seconds, when was the pail half full? Explain your answer.

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129)  Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.


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130)  Julia has a bucket of water that weighs 10lbs. The total weight is 99% water. She leaves the bucket outside overnight and some of the water evaporates, in the morning the water is only 98% of the total weight. What is the new weight?

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131)  Take a look at the following sums:
1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25

a. Come up with a conjecture about the sum when you add the first n odd numbers. For example, when you added the first 5 odd numbers (1 + 3 + 5 + 7 + 9), what did you get? What if wanted to add the first 10 odd numbers? Or 100?
b. Can you think of a geometric interpretation of this pattern? If you start with one square and add on three more, what can you make? If you now have 4 squares and add on 5 more, what can you make?
c. Is there a similar pattern for adding the first n even numbers? 2 = 2
2 + 4 = 6
2 + 4 + 6 = 12
2 + 4 + 6 + 8 = 20


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132)  Lucy has taken four tests in math class and has an average of 85.
i. What score would she have to get on her fifth test to have an average of 88?
ii. Can she get an average of 90? Explain.

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133)  Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is running at 5 feet per second and Claire is running at 3 feet per second.
i. After how many seconds will Sophie catch Claire?
ii. If the race is 500 feet, who wins?

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134)  An ancient Greek was said to have lived 1/4 of his live as a boy, 1/5 as a youth, 1/3 as a man, and spent the last 13 years as an old man. How old was he when he died?

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135)  I HAVE $11.60, all dimes and quarters, in my pocket. I have 32 more dimes than quarters. how many dimes, and how many quarters do i have?

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136)  If f(x) = 3x +1 and g(x) = x2 + 2x, find x when f(g(x)) = 10

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137)  Sound travels about 340 m/s. The function d(t) = 340t give the distance d(t),in meters., that sound travel in T seconds.
How far goes sound traveling 59s?

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138)  The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number by 18. What is the number?

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139)  Lena purchased a prepaid phone card for $15. Long distance calls cost 24 cents a minute using this card. Lena used her card only once to make a long distance call. If the remaining credit on her card is $4.92, how many minutes did her call last?

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140)  Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse is 6 years older than Alex. The sum of their ages is 31 years. Jow old is ech one of them?

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141)  A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel?

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142)  Two mechanics worked on a car. the first mechanic worked for 5 hours snd the second mechanic worked for 15 hours. Together they charged a total of $2375. What was the rate charged per hour by each mechanic if the sum of the two rates was $235 per hour?

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143)  At the end of the day, a bakery had 1/2 of a pie left over. The 4 employees each took home the same amount of leftover pie. How much pie did each employee take home?

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144)  There are 480 calories per hour. An officer swims 1.5 hours for 30 days. How many calories is that?

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