# How many rolls does the bank need to collect to have a 99 percent chance of a net loss

A bank accepts rolls of pennies and gives 50 cents credit to

a customer without counting the contents. Assume that a roll contains 49

pennies 30 percent of the time, 50 pennies 60 percent of the time, and 51

pennies 10 percent of the time.

(a) Find the expected value and the variance for the amount

that the bank loses on a typical roll.

(b) Estimate the probability that the bank will lose more

than 25 cents in 100 rolls.

(c) Estimate the probability that the bank will lose exactly

25 cents in 100 rolls.

(d) Estimate the probability that the bank will lose any

money in 100 rolls.

(e) How many rolls does the bank need to collect to have a

99 percent chance of a net loss?