Where do Canada's most clever people live? Who wins the IQ battle of the sexes? We found out on March 18, 2007. "Test the Nation" was the biggest survey ever conducted to see just how smart Ca- nadians are. In this live two-hour special, 1.5 million Canadians participated in a real- time interactive IQ test. Viewers took the test in the comfort of their own homes, on the Internet or with pen and paper, while seven teams-tattoo artists, millionaires, fitness instructors, surgeons, mayors, talk jocks and celebrities-exercised their grey matter in CBC's Toronto studio. Suppose that 20% of Canadians scored above average (that is, scoring 110 or more). You took a random sample of n = 64 and recorded their IQ scores.

a. What are the mean and standard deviation of sample proportion p, the sample pro- portion of individuals who scored above average?

b. Is the distribution of p approximately normal? Justify your answer.

c. What is the probability that the sample proportion p exceeds 18%?

d. What is the probability that the sample proportion p lies between 19% and 23%?

e. Ninety-nine percent of the time, the sample proportion two limits? would lie between what

f. What might you conclude if the sample proportion were as small as 10%? g. Would a value of p = 0.35 be considered unusual? Justify your answer.