1. The heights of 18-year-old females are approximately normally distributed with a mean of 64 inches and a standard deviation of 3 inches.
a. What is the probability that an 18-year-old woman selected at random is between 63 and 65 inches tall?
b. Suppose samples of 25 18-year-old females are taken at a time. Describe the sampling distribution of the sample mean and compute the mean and standard deviation of this sampling distribution.
c. Find the z-score corresponding to a sample mean of 66 inches for a sample of 25 females.
d. Find the probability that a sample mean from a sample like this would be higher than 66 inches.
e. Based on the probability found in the previous part, would a sample like this be unusual?
f. If a random sample of 25 18-year-old females is selected, what is the probability that the mean height for this sample is between 63 and 65 inches?