The upper leg length of 20- to 29-year-old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm.

(a) What is the probability that a randomly selected 20- to 29-year-old male has an upper leg length that is less than 40 cm?

(b) A random sample of 9 males who are 20 to 29 years old is obtained. What is the probability that the mean upper leg length is less than 40 cm?

(c) What is the probability that a random sample of 12 males who are 20 to 29 years old results in a mean upper leg length that is less than 40 cm?

(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result.

(e) A random sample of 15 males who are 20 to 29 years old results in a mean upper leg length of 46 cm. Do you find this result unusual? Why?