Question

the number of accidents on a particular highway average 4.4 per year. assume that the number of accidents follows a Poisson distribution. what is the probability that there are exactly four accidents next year? what is the probability that there are more than three accidents next year?

Answer 1

= 4.4

P(X = x) = e/x!

a) P(X = 4) = e^(-4.4) * (4.4)^4/4! = 0.1917

b) P(X > 3) = 1 - P(X < 3)

                  = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

                  = 1 - (e^(-4.4) * (4.4)^0/0! + e^(-4.4) * (4.4)^1/1! + e^(-4.4) * (4.4)^2/2! + e^(-4.4) * (4.4)^3/3!)

                  = 1 - 0.3594

                  = 0.6406