The number of bank mergers in the 1990s far exceeded any previous 10-year period in US. history. As mergers created larger and larger banks, many customers charged the mega-banks with becoming more and more impersonal in dealing with customers. A recent poll by the Gallup Organization found 20% of retail customers switched banks after their banks merged with another

(Bank Marketing, Feb. 1999). One year after the acquisition of First Fidelity by First Union, a random sample of 25 retail customers who had banked with First Fidelity were questioned. Let x be the number of those customers who switched their business from First Union to a different bank.

a. What assumptions must hold in order for x to be a binomial random variable? In the remainder of this exercise, use the data from the Gallop Poll to estimatep.

b. What is the probability that x 5 lo?