Chapter 7, Problem 2PS

Given a normal distribution with $\mu =50\text{and}\sigma =5,$ if you select a sample of $n=100,$ what is the probability that $\text{<mover accent="true"> X <mo> ¯ </mo> </mover>}$ is

a. less than 47?

b. between 47 and 49.5?

c. above 51.1?

d. There is a 35% chance that $\bar{X}$ is above what value?