Your company is running an audit on the Sleaze Company. Because Sleaze has a bad habit of overcharging its customers, the focus of your audit is on checking whether the billing amounts on its invoices 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.
a. If you randomly sample 200 of Sleaze’s invoices, what is the probability that you will find at least 15 invoices that overcharge the customer? What is the probability you won’t find any that undercharge the customer?
b. Find an integer k such that the probability is at least 0.99 that you will find at least k invoices that overcharge the customer.