Suppose that, according to a recent census, 29% of all families in the province of Quebec are common-law couples. You survey 100 families in the city of Montreal in order to assess the purchasing preferences of common-law couples.

a) What is the probability that the percentage of commonlaw couples in your Montreal sample is higher than 30%? State your assumptions clearly.

b) You need to find 100 common-law couples in Montreal to interview in detail. Would a sample size of 400 families be sufficient for you to be confident of finding these 100 couples? State your assumptions and reasons clearly.