A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and standard deviation equal to 16.

a. Give the mean and standard deviation of the (repeated) sampling distribution of x-bar.

b. Describe the shape of the sampling distribution of x-bar. Does your answer depend on the sample size?

c. Calculate the standard normal z -score corresponding to a value of x-bar = 16.

d. Calculate the standard normal z -score corresponding to x-bar = 23.

e. Find P(x-bar < 16).

f. Find P(x-bar > 23).

g. Find P(16 < x-bar < 23).