Question

An insurance company receives nine claims per week, on average. Use this information to answer the next two questions. What is the probability that exactly 7 claims will be received in one week

Answer 1

P(X = 7) = 0.11712

Explanation:

From the information given:

Average no. of claims received per week λ = 9

The required probability that exactly 7 claims will be received is determined by applying the Poisson distribution formula:

`P(X=x) = (\lambda ^x e^(-\lambda))/(x!)`

`P(X=7) = (9 ^7 e^(-9))/(7!)`

`P(X=7) = (4782969 *1.23409804 * 10^(-4))/(5040)`

`P(X=7) = (590.2652672)/(5040)`

P(X = 7) = 0.11712