Millions of suburban commuters use the public transit system (e.g., subway trains) as an alternative to the automobile. While generally perceived as a safe mode of transportation, the average number of deaths per week due to public transit accidents is 5 (Bureau of Transportation Statistics, 2015).

a. Construct arguments both for and against the use of the Poisson distribution to characterize the number of deaths per week due to public transit accidents.

b. For the remainder of this exercise, assume the Poisson distribution is an adequate approximation for x, the number of deaths per week due to public transit accidents. Find E(x) and the standard deviation of x.

c. Based strictly on your answers to part b, is it likely that more than 12 deaths occur next week? Explain.

d. Find P(x > 12). Is this probability consistent with your answer to part c? Explain.