Banks that merge with others to form "mega-banks" sometimes leave customers dissatisfied with the impersonal service. A poll by the Gallup Organization found 20% of retail customers switched banks after their banks merged with another. One year after the acquisition of First Fidelity by First Union, a random sample of 250 retail customers who had banked with First Fidelity were questioned. Let p̂ be the proportion of those customers who switched their business from First Union to a different bank.

a. Find the mean and the standard deviation of p̂.

b. Calculate the interval E(p̂) ± 2σp̂.

c. If samples of size 250 were drawn repeatedly a large number of times and p̂ determined for each sample, what proportion of the p̂ values would fall within the interval you calculated in part c?