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A commercial bank issues three versions of its credit card: Classic, Gold and Platinum. A customer's application for a credit card may be refused because of the customer's poor credit rating.
a) The proportion of customers who are refused the Classic version of the bank's credit card is 0.275. Using a binomial distribution model, calculate the probability that from a random sample of 10 customers applying for the classic version, exactly two applications are refused.
b) The proportion of customers who are refused the Gold version of the bank's credit card is 0.65. Using the binomial distribution model again, determine the probability that, from a random sample of 40 customers applying for the Gold version, the number of applications that are accepted is; i. Not more than 15; ii. At least 10 but at most 20.
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