Probability based on Poisson distribution.

Increased research and discussion have focused on number of illnesses involving the organism Escherichia coli (01257: H&), 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, which spread the bacteria into a spinach field in California, sickened 204 people in 26 states and 1 Canadian province. 6 bacteria Outbreaks have occurred at a rate of 2.5 per 100,000. Let us assume that this rate has not changed.

a. What is the possibility 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. in the order of 95 percent of occurrences of E. coli involve at most how many cases?