At a major credit card company, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are 60 %, 30 %, and 10 %, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. We are interested in whether the percentages for this promotion are different from the historical percentages.

a) What is the expected number of customers applying for each type of card in this sample if the historical proportions are still true?

b) Compute the 2 statistic.

c) How many degrees of freedom does the 2 statistic have?