In a certain city, the number of potholes on a major street follows a Poisson distribution with a rate of 3 per mile. Let X represent the number of potholes in a two-mile stretch of road. Find

a. P(X = 4)

b. P(X ≤ 1)

c. P(5 ≤ X<8)

d. μX

e. σX

Step 1 of 6</p>

Let X represents no. of potholes

Here X follows poisson distribution with rate of 3 per mile

So

The pmf of poisson distribution is P(x)=, X=0,1,2,..............

Step 2 of 6</p>

a)P(X=4)=

=

=0.168

Hence P(X=4)=0.168

Step 3 of 6</p>

b) P(XP(0)+P(1)

For that we need to find p(0) and p(1)

P(0)=

=0.0498

P(1)=

=0.1494