Question

scores on the gre (graduate record examination) are normally distributed with a mean of 519 and a standard deviation of 74. use the 68 - 95 - 99.7 rule to find the percentage of people taking the test who score between 371 and 667. the percentage of people taking the test who score between 371 and 667 is %.

Explanation:

Step1: Calculate number of standard - deviations from the mean

First, find how many standard - deviations 371 and 667 are from the mean. Let $\mu = 519$ and $\sigma=74$.
For $x = 371$, $z_1=\frac{371 - 519}{74}=\frac{-148}{74}=-2$.
For $x = 667$, $z_2=\frac{667 - 519}{74}=\frac{148}{74}=2$.

Step2: Apply the 68 - 95 - 99.7 Rule

The 68 - 95 - 99.7 Rule states that for a normal distribution, approximately 95% of the data lies within 2 standard - deviations of the mean. That is, $P(-2\sigma

Answer:

95