Question

An accident is observed on an average” x “cars on a busy road. Assume that the distribution of accidents follow Poisson distribution, then find the following probabilities: (Use Dataset F to find the ‘x’ and’ a ‘)

a. There will be at most ‘a-1’ accidents.

b. There will be exactly ‘a’ accidents.

c. There will be at least ‘a-3 ‘accidents

x	a
3.9	8

Answer 1

a.

P(X 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

=  0.02024191 + 0.07894345 + 0.15393974 + 0.20012166 + 0.19511862 + 0.15219252 + 0.09892514 + 0.05511543

= 0.9545985

b.

P(X = 8) =

= 0.02686877

c.

P(X 5) = 1 - P(X < 5) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4))

= 1 - (0.02024191 + 0.07894345 + 0.15393974 + 0.20012166 + 0.19511862) (From part(a))

= 0.3516346