Suppose P is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and P has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval ?

A 8/(2e³)

B 9/(2e³)

C 17/(2e³)

D 26/(2e³)

Answer & Explanation
Answer: Option [C]

p is the number of cars per minute passing through a certain road junction.

The random variable P follows Poisson distribution with mean 3.

So, Prob(P = r)=

We have to determine probability of observing fewer than 3 cars.

So, r=0,1,2

Prob(P=0) + Prob(P=1) + Prob(P=2)

+ +

=1/e³[1+3+9/2]

=17/2e³