At a major credit cardbank, the percentages of people who historically apply for theSilver, Gold and Platinum cards are 60 %,30 %and 10 %10respectively. In a recent sample of customers responding to apromotion, of 200customers,111applied forSilver,51for Gold and 38for Platinum. Is there evidence to suggest that the percentages for this promotion may be different from the historicalproportions?

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

b) Compute the 2statistic.

c) How many degrees of freedom does the 2statistichave?