Question

The average number of claims per hour made to an insurance company is 3.

a. What is the probability that over the next hour 4 claims will be placed?

b. What is the probability that over the next 3 hours 6 claims will be placed?

Answer 1

Explanation:

We have it that x follows a poisson distribution.

λ is equal to 3

The poisson distribution is given by:

P(x) = e^-λ * λ^X/X!

λ = 3

X = 4

A. The question had already given us the X value to be 4

p(x = 4)

= e^-3 x 3⁴/4!

= e^-3 = 0.001

3⁴= 34

4! = 81

putting all values into p(x=4)

= .001x81/24

= 0.1680

b. for 3 good hours, we will have lamda to be;

3x3 = 9

p(x = 6)

= e^-9 * 9⁶/6!

= 0.0911