In the results published by Wright et al. [A-2] based on data from the 1999-2000 NHANES study referred to in Exercises 5.4.1 and 5.4.2, investigators reported on their examination of iron levels.

A) The mean iron level for women ages 20-39 years was 13.7 mg with an estimated standard deviation of 8.9 mg. Using these as population values for women ages 20-39, find the probability that a random sample of 100 women will have a mean iron level less than 12 mg. Show all intermediate steps.

B) The mean iron level for men between the ages of 20 and 39 years is 17.9 mg with an estimated standard deviation of 10.9 mg. Using 17.9 and 10.9 as population parameters, find the probability that a random sample of 120 men will have a mean iron level higher than 19 mg. Show all intermediate steps.

C) Using the information in Parts A and B, and assuming independent random samples of size 100 and 120 for women and men, respectively, find the probability that the difference in sample mean iron levels is greater than 5 mg. Please use difference in (men - women). Show all intermediate steps.