5.55 The National Maximum Speed Limit (NMSL) of 55 miles per hour has been in force in the United States since early 1974. The benefits of this law have been studied by D.B. Kamerud

(Transportation Research, 17A, no. 1, 1983, pp.

51–64), who reports that the fatality rate for interstate highways with the NMSL in 1975 is approximately 16 per 109 vehicle miles.

a Find the probability of at most 15 fatalities occurring in 109 vehicle miles.

b Find the probability of at least 20 fatalities occurring in 109 vehicle miles.

(Assume that the number of fatalities per vehicle mile follows a Poisson distribution.)