A family of mutual funds maintains a service that allows clients to switch money among accounts through a telephone call. It was estimated that 3.2% of callers either get a busy signal or are kept on hold so long that they may hang up. Fund management assesses any failure of this sort as a $10 goodwill loss. Suppose that 2,000 calls are attempted over a particular period.
a. Find the mean and standard deviation of the number of callers who will either get a busy signal or may hang up after being kept on hold.
b. Find the mean and standard deviation of the total goodwill loss to the mutual fund company from these 2,000 calls.