Suppose that in the general population of men between 65 and

Suppose that in the general population of men between 65 and 70 years old, 60 percent have a resting systolic blood pressure over 130 mm Hg, considered a high blood pressure. Consider a sample of 20 men randomly sampled from this population. For each one, it is determined whether or not they have high blood pressure. a. What, under appropriate conditions, is the exact probability distribution of the number of men in the sample who have high blood pressure? Give the name of the distribution and the numerical values of the parameters it depends on. Explain the three conditions that must be satisfied to justify using this distribution, and comment on whether or not each one is satisfied. b. Give the mean and standard deviation of the distribution in part a, and show how they are calculated. c. Use the exact probability distribution to calculate the probability that from 10 to 12 of the men (i.e. 10, 11, or 12 men) have high blood pressure. Explain how the calculation is done, show the mathematical formula used for the calculation, and give the numerical result. d. State the conditions that must be satisfied to use a Normal approximation to the exact distribution, and explain why each one is or is not satisfied. e. Use a Normal approximation to the probability distribution in part a. to obtain an approximate answer to part c. Do calculations both with and without the continuity correction. Explain how the calculations are done using the Normal distribution. For each of the two calculations, find the percent error of the approximation to the exact answer in part c. f. Would the Normal approximation be more accurate if the number of men sampled was 30 instead of 20? Justify your answer

Solution

a) nmormal distribution

b) mean = 0.60 * 20 = 12

SD = srqt ( 0.60*0.40*20 ) = 2.19

c)

for the other literals

I can gladly help you but you should post it in a new question