MBNA offers personal and business credit cards, loans, and savings products. It was bought by Bank of America in June 2005. One of the selling points for MBNA was its position relative to the rest of the credit card industry.

MBNA’s customers’ average annual spending per active account before the purchase was $6,920. To demonstrate its relative position in the industry, MBNA’s CFO, H.

Vernon Wright, might authorize a survey producing the following data on the annual spending, to the nearest dollar, of accounts in the industry:

3,680 6,255 6,777 7,412 4,902 5,522 5,190 7,976 4,116 3,949 6,814 2,264 4,991 5,353 5,914 5,828 6,059 6,354 6,193 5,648 6,117 7,315 6,458 4,973 6,554 1,926 4,395 5,341 4,921 6,268 4,061 4,777 5,876 5,984 3,381 5,441 4,268 7,657 6,449 4,821 This sample is contained in the file labeled ASpending.

a. Conduct a hypothesis test to determine if MBNA has larger average annual spending per active account than the rest of the credit card industry. Use a p-value approach and a significance level of 0.025.

b. If the industry’s annual spending per active account was normally distributed with a mean of $5,560 and a standard deviation of $1,140, determine the probability that a randomly chosen account would have an annual spending larger than MBNA’s.