Suppose that the mean value of interpupillary distance for all adult males is 65 mm, and the population standard deviation is 5 mm. Assume that the distribution of interpupillary distances is approximately normal.
a) If a sample of 22 adult males is selected, what is the probability that the sample average distance x? is between 64.3 and 66.4 mm?
b) Given that the sample size in part (a) is small, explain in a complete sentence why we know that the sampling distribution of x? is normally distributed.