7.71 Suppose a random sample of n = 5 observations is selected from a population that is normally distrib- uted, with mean equal to 1 and standard deviation equal to 0.36.

a. Give the mean and standard deviation of the sam- pling distribution of .x.

b. Find the probability that exceeds 1.3.

c. Find the probability that the sample mean x is less than 0.5.

d. Find the probability that the sample mean deviates from the population mean u = 1 by more than 0.4.