The Public Citizen's Health Research Group studied the serious disciplinary actions that were taken during a recent year on nonfederal medical doctors in the United States. The national average was 2.92 serious actions per 1,000 doctors. The state with the lowest number was South Carolina, with 1.18 serious actions per 1,000 doctors.

Assume that the numbers of serious actions per 1,000 doctors in both the United States and in South Carolina are Poisson distributed.

a. What is the probability of randomly selecting 1,000 U.S. doctors and finding no serious actions taken?

b. What is the probability of randomly selecting 2,000 U.S. doctors and finding six serious actions taken?

c. What is the probability of randomly selecting 3,000 South Carolina doctors and finding fewer than seven serious actions taken?