Question

A car insurance officer can handle up to 2 claims each working day without significant delays. The average number of claims per working day is 1.7. Assume the number of claims can be modeled by a Poisson distribution.

1. What is the probability that the insurance officer will have exactly 3 claims in a day.

2. What is the probability that the insurance officer will have fewer than 44 claims in a month? Assume the month has 22 working days.  

c. Find the mean and standard deviation for the number of claims per working day.

Answer 1

a)
Here, λ = 1.7 and x = 3
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 3)
P(X = 3) = 1.7^3 * e^-1.7/3!
P(X = 3) = 0.1496
Ans: 0.1496

b)
λ = 1.7*22 = 37.4

P(X < 44) = 0.841

c)
mean = 1.7
std. dev. = sqrt(1.7) = 1.3038