Given a normal distribution with μ = 100 and σ = 15, calculate the 68-95-99.7 rule, or three-sigma rule, or empirical rule ranges
Calculate Range 1:
Range 1, or the 68% range, states that 68% of the normal distribution values lie within 1 standard deviation of the mean68% of values are within μ ± σ
μ ± σ = 100 ± 15
100 - 15 <= 68% of values <= 100 + 15
85 <= 68% of values <= 115
Calculate Range 2:
Range 2, or the 95% range, states that 95% of the normal distribution values lie within 2 standard deviations of the mean95% of values are within μ ± 2σ
μ ± 2σ = 100 ± 2(15)
100 - 2 x 15 <= 95% of values <= 100 + 2 x 15
100 - 30 <= 95% of values <= 100 + 30
70 <= 95% of values <= 130
Calculate Range 3:
Range 3, or the 99.7% range, states that 99.7% (virtually ALL) of the normal distribution values lie within 3 standard deviations of the mean99.7% of values are within μ ± 3σ
μ ± 3σ = 100 ± 3(15)
100 - 3 x 15 <= 99.7% of values <= 100 + 3 x 15
100 - 45 <= 99.7% of values <= 100 + 45
55 <= 99.7% of values <= 145
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What is the Answer?
55 <= 99.7% of values <= 145
How does the Normal Distribution Calculator work?
Free Normal Distribution Calculator - Calculates the probability that a random variable is less than or greater than a value or between 2 values using the Normal Distribution z-score (z value) method (Central Limit Theorem).
Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability
This calculator has 4 inputs.
Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability
This calculator has 4 inputs.
What 1 formula is used for the Normal Distribution Calculator?
What 9 concepts are covered in the Normal Distribution Calculator?
- distribution
- value range for a variable
- empirical rule
- Provides estimate for the spread of data in a normal distribution. 68% of the data will fall within one standard deviation of the mean. 95% of the data will fall within two standard deviations of the mean. 99.7% of the data will fall within three standard deviations of the mean
- event
- a set of outcomes of an experiment to which a probability is assigned.
- mean
- A statistical measurement also known as the average
- normal distribution
- an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
- probability
- the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes - standard deviation
- a measure of the amount of variation or dispersion of a set of values. The square root of variance
- variance
- How far a set of random numbers are spead out from the mean
- z score
- the number of standard deviations from the mean a data point is. Also known as a standard score
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