Increased research and discussion have focused on the number of illnesses involving the organism Escherichia coli (01257:H7), which causes a breakdown of red blood cells and intestinal hemorrhages in its victims. According to the Center for Disease Control, an estimated 73,000 cases of E. coli infection and 61 deaths occur in the United States each year. A 2006 outbreak traced to wild pigs, who spread the bacteria into a spinach field in California, sickened 204 people in 26 states and 1 Canadian province. Outbreaks have occurred at a rate of 2.5 per 100,000. Let us suppose that this rate has not changed.

a. What is the probability that at most five cases of E.coli per 100,000 are reported in California this year?

b. What is the probability that more than five cases of E. coli are reported in California this year?

c. Approximately 95% of occurrences of E. coli involve at most how many cases?