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Sheila's doctor is concerned that she may suffer fromgestational diabetes (high blood glucose levels during pregnancy).There is variation both in the actual glucose level and in theblood test that measures the level. A patient is classified ashaving gestational diabetes if the glucose level is above 140miligrams per deciliter (mg/dl) one hour after having a sugarydrink. Sheila's measured glucose level one hour after the sugarydrink varies according to the Normal distribution with μμ = 125mg/dl and σσ = 15 mg/dl.

(a) If a single glucose measurement is made, what is theprobability that Sheila is diagnosed as having gestationaldiabetes?
(b) If measurements are made on 7 separate days and the mean resultis compared with the criterion 140 mg/dl, what is the probabilitythat Sheila is diagnosed as having gestational diabetes?

Andrew plans to retire in 36 years. He plans to invest part ofhis retirement funds in stocks, so he seeks out information on pastreturns. He learns that over the entire 20th century, the real(that is, adjusted for inflation) annual returns on U.S. commonstocks had mean 8.7% and standard deviation 20.2%. The distributionof annual returns on common stocks is roughly symmetric, so themean return over even a moderate number of years is close toNormal.

(a) What is the probability (assuming that the past pattern ofvariation continues) that the mean annual return on common stocksover the next 36 years will exceed 11%?
(b) What is the probability that the mean return will be less than4%?