QUARTER 1: ASSIGNMENT 2

The disribution of heights of adult American men is approximately normal with population mean 69 inches and population standard deviation 2.5 inches.
(a) Show the notation that correctly describes the distribution of adult American men's heights.
(b) Draw the Curve to appropriately describe the distribution (appropriately label the x-axis)
(c) What percent of men are taller than 74 inches?
(d) Between what heights do all middle 95% of men fall?
(e) What percent of men are shorter than 66.5 inches.
(f) What is the probability that a randomly selected man would have a height within one standard eviation of the mean?
(g) A height of 71.5 inches corresponds to what percentile of adult male American heights?
(h) What is the z-score for a man with a height of 73 inches?
(i) A man has a height of 63 inches. How many standard deviation away from the mean is 63 inches?
(j) Is the man's height of 63 inches considered unusual? Explain.
(k) Suppose a man's height had an associated z-score of z = 5.62. How tall is this man in inches. How tall is he in feet?

2. Suppose the lengths of a human pregnancies are normally distributed.
(a) A woman's pregnancy length had a z-score of z = 1.5. Was this pregnancy longer or shorter than the average pregnancy? Explain.
(b) A woman's pregnancy length had a z-score of z = -7.00. Comment.

3. The army reports that the distribution of head circumferences among soldiers is normally distributed with population mean 22.8 inches and population standard deviation 1.1 inches.
(a) How many, of 1500 soldiers, would be expected to fit helmets prepared for individuals with head circumferences 23.9 and larger?
(b) Suppose 5000 solders were sent 5000 helmets that fit head circumferences between 21.7 and 25 inches. How many solders would be expected order new helmets?
(c) If the unused helmets are shipped back at a cost of $0.08 per helmet. What is the expected cost for shipping the unused helmets?
(d) Suppose it cost $0.08 per helmet to ship helmets to the soldiers and the same price to ship helmets back as described in part (b). Suppose, also, that it cost $0.04 per solder to measure the head sizes of soldiers (mostly administrative and time costs). Which is more costly (i) to send a batch of 5000 helmets to fit sizes 21.7 to 25 and then measure only those who need new helmets or (ii) to measure all solders first and then return the unused and send the correct sizes? Show.