Medicare reimbursement regulations require no more than a 4% error rate in invoice coding from a service provider. You draw a random same of 75 invoices and, upon audit, find that there are 5 errors in the 75 invoices sampled.

(a) If the true billing error rate for this service provider were no higher than 4%, what is the probability of having observed 5, or more, errors in your sample?

(b) Suppose that the true error rate is 4%. What is the interval that is plus, or minus, two standard deviations from the expected value?

(c) If a provider's true error-coding rate were 4%, find the probability that a sample of 75 will result in between 1 to 5 coding errors, i.e., find