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

Answer:

P(X = 7) = 0.11712

Step-by-step 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:

$P(X=x) = \dfrac{\lambda ^x e^{-\lambda}}{x!}$

$P(X=7) = \dfrac{9 ^7 e^{-9}}{7!}$

$P(X=7) = \dfrac{4782969 \times1.23409804 \times 10^{-4}}{5040}$

$P(X=7) = \dfrac{590.2652672}{5040}$

P(X = 7) = 0.11712