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?


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