At night and at a particular highway location police patrols

At night and at a particular highway location, police patrols assess an average number of 2.2 speed limit violations per hour. Calculate the probability that a patrol does not detect any violation within time spans of

(a) 30 minutes,

(b) 60 minutes,

(c) 90 minutes.

Solution

X is number of speed limit violation per houra. F

X~P(2.2)

a.

X~P(2.2/2) ~P(1.1)

P(X=0) = poisson(0,1.1,0)=0.332871

b.

X~P(2.2)

P(X=0) = 0.110803

c.

X~P(3.3)

P(X=0) = poisson(0,3.3,0) = 0.036683