3. Increased research and discussion have focused on the number of illnesses involving the organism Escherichia coli which causes a breakdown of red blood cells and intestinal hemorrhages in its victims. Sporadic outbreaks of E. coli have occurred in Colorado at a rate of 2.5 per 100,000 for a period of 2 years. Let us suppose that this rate has not changed. a. Can x, the number of cases of E. coli in a year, be treated as a binomial random variable? Why or why not? b. Can x, the number of cases of E. coli in a year, be treated as a Poisson random variable? Why or why not? c. Can the probability of x, the number of cases of E. coli in a year, be calculated using the Poisson approximation to the binomial? Why or why not? d. Calculate P(x-5) using all of the above methods, if applicable.

3. Increased research and discussion have focused on the number of illnesses involving the organism Escherichia coli which causes a breakdown of red blood cells and intestinal hemorrhages in its victims. Sporadic outbreaks of E. coli have occurred in Colorado at a rate of 2.5 per 100,000 for a period of 2 years. Let us suppose that this rate has not changed. a. Can x, the number of cases of E. coli in a year, be treated as a binomial random variable? Why or why not? b. Can x, the number of cases of E. coli in a year, be treated as a Poisson random variable? Why or why not? c. Can the probability of x, the number of cases of E. coli in a year, be calculated using the Poisson approximation to the binomial? Why or why not? d. Calculate P(x-5) using all of the above methods, if applicable.