30 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.

b. Describe the shape of the sampling distribution of x.

Does your answer depend on the sample size?

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

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

e. Find P(x 6 16).

f. Find P(x 7 23).

g. Find P(16 6 x 6 23).