MBNA Canada’s affiliates program allows other organizations to offer credit cards to their members. The Toronto Blue Jays and the Edmonton Eskimos both use MBNA’s affiliates program, as does the Canadian Automobile Association. Whenever a member of one of these organizations makes a purchase using the card, MBNA processes the transaction and gives a certain percentage of the value of the transaction to the organization.

Suppose you’re working for a sports club that’s considering joining MBNA’s affiliates program. You know that many of your members would be proud to use a card with your logo on it, but you also know that many of them already have other credit cards, and you don’t want to annoy them by offering them another one if they don’t want it. The president of the club decides to become an MBNA affiliate only if the proportion of members signing on for the new card is over 3%. You know from a colleague in another club that they had a take-up rate for affiliate cards of 4.3%. You think the other club is similar to yours and decide to survey 100 of your members to find out how many would accept the new card.

What is the probability that more than 3% of your sample would accept the new card? State your assumptions clearly. Indicate on a graph how this probability changes if you increase your sample size in increments of 100 from 100 to 1000. Approximately what sample size do you recommend?