problem library | Page 3 | MathCelebrity Forum

# problem library

1. ### You have \$250,000 in an IRA (Individual Retirement Account) at the time you retire. You have the op

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 Fund A and Fund B to produce an annual interest...
2. ### If you buy a computer directly from the manufacturer for \$3,509 and agree to repay it in 36 equal in

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? Determine the monthly payment The monthly payment is...
3. ### What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.4%? Round

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. Set up the accumulation equation: (1+i)^365 = 1.054 Take the natural log of each side 365 * Ln(1 + i) = 1.054 Ln(1 + i) = 0.000144089 Use each...
4. ### You can afford monthly deposits of \$270 into an account that pays 3.0% compounded monthly. How long

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. Set up our accumulation expression: 270(1.03)^n = 11100 1.03^n = 41.1111111 Take the natural log of both sides...
5. ### Suppose that Sn = 3 + 1/3 + 1/9 + ... + 1/3(n-2)

Suppose that Sn = 3 + 1/3 + 1/9 + ... + 1/3(n-2) a) Find S10 and S∞ b) If the common difference in an arithmetic sequence is twice the first term, show that Sn/Sm = n^2/m^2 a) Sum of the geometric sequence is a = 3 and r = 1/3 (a(1 - r)^n)/(1 - r) (3(1 - 1/3)^9)/(1 - 1/3) S10 =...
6. ### A man stands at point p, 45 metres from the base of a building that is 20 metres high. Find the angl

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. Draw a right triangle ABC where Side A is from the bottom of the building to the man and Side B is the bottom of the building to the top of...
7. ### Rearrange the following equation to make x the subject, and select the correct rearrangement from th

Rearrange the following equation to make x the subject, and select the correct rearrangement from the list below 3x + 2y 1 -------- = --- 4x + y 3 x = 7y/13 x = 7y/5 x = -7y x = -3y x = 3y/5 x = -5y/13 x = -y Cross multiply: 3(3x - 2y) = 4x + y Multiply the left side...
8. ### 4 people like ketchup, 1 person likes tomato. How many people like ketchup or tomato?

4 people like ketchup, 1 person likes tomato. How many people like ketchup or tomato? Or means we add. We want to add people that like both ketchup and tomatoes. 4 ketchup + 1 tomato = 5 total people
9. ### A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population sta

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. 2902 < u < 3098 using our confidence interval for the mean calculator
10. ### The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a) What i

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...
11. ### Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opp

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)...
12. ### Prizes hidden on a game board with 10 spaces. One prize is worth \$100, another is worth \$50, and tw

Imagine you are in a game show. 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...
13. ### CCP Stat Club is sending a delegate of 2 members to attend the 2015 Joint Statistical Meeting in Sea

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? 10C2 = 45 shown on our Combinations Calculator
14. ### There are 1000 juniors in a college. Among the 1000 juniors, 200 students are taking STAT200, and 10

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...
15. ### A fair coin is tossed 4 times. a) How many outcomes are there in the sample space? b) What is the pr

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...
16. ### A random sample of STAT200 weekly study times in hours is as follows: 2 15 15 18 30 Find the sam

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.) 9.98 using our standard deviation calculator
17. ### A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afte

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) | Frequency | Relative Frequency 1.0 - 1.9 | 2 | ? 2.0 - 2.9 | 8 | ? 3.0...
18. ### True or False (a) The normal distribution curve is always symmetric to its mean. (b) If the variance

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 A<sup>c</sup>)=1, where A<sup>c</sup> is the complement of A. (d) In a hypothesis testing, if the...
19. ### Write a model that utilizes all three explanatory variables with no interaction or quadratic terms.

Write a model that utilizes all three explanatory variables with no interaction or quadratic terms. Choose the correct answer below. A. y i = B<sub>0</sub> + B1x1 + B2x2 + B3x3 + e i B. y i = B<sub>0</sub> + B1x1 + B2x2 + B3x3x2 + e i C. y i = B1x1 + B2x2 + B3x3 + ei D. None of the above...
20. ### The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered t

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...