Your company is running a Medicare audit on Sleaze Hospital. Because Sleaze has a history of overbilling, the focus of your audit is on checking whether the billing amounts are correct. Assume that each invoice is for too high an amount with probability 0.06 and for too low an amount with probability 0.01 (so that the probability of a correct billing is 0.93). Also, assume that the outcome for any invoice is probabilistically independent of the outcomes for other invoices.

Suppose that when Sleaze overcharges Medicare, the distribution of the amount overcharged (expressed as a percentage of the correct billing amount) is normally distributed with mean 15% and standard deviation 4%.