The manager for State Bank and Trust has recently examined the credit card account balances for the customers of her bank and found that 20% have an outstanding balance at the credit card limit. Suppose the manager randomly selects 15 customers and finds 4 that have balances at the limit. Assume that the properties of the binomial distribution apply.
a. What is the probability of finding 4 customers in a sample of 15 who have “maxed out” their credit cards?
b. What is the probability that 4 or fewer customers in the sample will have balances at the limit of the credit card?