Answer
a. 0.159
b. 0.00135
Work Step by Step
Given $\mu=40000, \sigma=5000$
a. An individual graduate will have a salary over 45,000.
$z(45000)=\frac{45000-40000}{5000}=1$
The probability above z=1 is 0.159
b. A group of nine graduates will have a group average over 45,000.
The sampling distribution will have the same mean but a new
standard deviation of 5000/3. The same value of 45000 will
correspond to a new z-score of 3, and the probability that
the group average over 45000 is 0.00135
