Question

e. $p(x < ?)=.75$

1. suppose that the distribution of scores on the graduate record exam (gre) is approximately normal, with a mean of $mu = 150$ and a standard deviation of $sigma = 5$. for the population of students who have taken the gre:

a. what proportion have gre scores less than 145?

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$. For part a, $x = 145$, $\mu=150$, and $\sigma = 5$. So $z=\frac{145 - 150}{5}=\frac{- 5}{5}=-1$.

Step2: Find the proportion from the standard normal table

We look up the z - score of - 1 in the standard - normal distribution table. The value corresponding to $z=-1$ is $0.1587$.

Answer:

The proportion of students with GRE scores less than 145 is $0.1587$.