Question

scores on the gre (graduate record examination) are normally distributed with a mean of 530 and a standard deviation of 108. use the 68 - 95 - 99.7 rule to find the percentage of people taking the test who score between 314 and 530. the percentage of people taking the test who score between 314 and 530 is %.

Explanation:

Step1: Calculate number of standard - deviations

First, find out how many standard deviations 314 is from the mean. Let $\mu = 530$ and $\sigma=108$. The formula for the z - score is $z=\frac{x - \mu}{\sigma}$. For $x = 314$, $z=\frac{314 - 530}{108}=\frac{-216}{108}=- 2$.

Step2: Apply the 68 - 95 - 99.7 Rule

The 68 - 95 - 99.7 Rule states that about 95% of the data lies within 2 standard deviations of the mean in a normal distribution, i.e., $P(-2\sigma

Answer:

47.5