Suppose that 10% of the people in a certain population have the eye disease glaucoma. For persons who have glaucoma, measurements of eye pressure X will be normally distributed with a mean of 25 and a variance of 1. For persons who do not have glaucoma, the pressure X will be normally distributed with a mean of 20 and a variance of 1. Suppose that a person is selected at random from the population and her eye pressure is measured.

a) Determine the conditional probability that the person has glaucoma given thatX=x.

b) For what values of x is the conditional probability in part (a) greater than 1/2?

A survey dating back to the 1990's suggested that Americans anticipated a reduction in living standards and that a steadily increasing consumption no longer might be as important as it was in the past. (Were they right?) Suppose that a poll of 2000 people indicated 1373 in favor of forcing a reduction in the size of American automobiles by legislative means. Would you expect to observe as many as 1373 in favor of this proposition if, in fact, the general public was split 50-50 on the issue?