Question

scores on the gre (graduate record examination) are normally distributed with a mean of 535 and a standard deviation of 122. use the 68 - 95 - 99.7 rule to find the percentage of people taking the test who score between 291 and 779.
the percentage of people taking the test who score between 291 and 779 is %.

Explanation:

Step1: Calculate number of standard - deviations from the mean

First, find how many standard - deviations 291 and 779 are from the mean of 535.
For \(x = 291\), \(z_1=\frac{291 - 535}{122}=\frac{- 244}{122}=- 2\)
For \(x = 779\), \(z_2=\frac{779 - 535}{122}=\frac{244}{122}=2\)

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 \(z=-2\) and \(z = 2\) standard - deviations of the mean.

Answer:

95