Show how you arrived at your solution on the answer sheet for full credit. Write neatly and be organized.
PROBLEM 5
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 72 inches and standard deviation 5 inches.
(a) What is the probability that an 18-year-old man selected at random is more than 71 inches tall? (Round your answer to four decimal places.) Draw the normal curve, label and shade the area. (5PTS)
(b) What is the probability that an 18-year-old man selected at random is less than 73 inches tall? (Round your answer to four decimal places.) Draw the normal curve, label and shade the area. (5PTS)
(c) If a random sample of twenty-five 18-year-old men is selected, what is the probability that the mean height \( x \) is between 71 and 73 inches? (Round your answer to four decimal places.)) Draw the normal curve, label and shade the area. (5PTS)