A random sample of n measurements was selected from a population with unknown mean m and known standard deviation s. Calculate a 95% confidence interval for m for each of the following situations:

a. n = 75, x = 28, s2 = 12

b. n = 200, x = 102, s2 = 22

c. n = 100, x = 15, s = .3

d. n = 100, x = 4.05, s = .83

e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a–d? Explain.