Question

On average, an insurance company receives 6 claims between 14:00 and 16:00 on a particular day. What is the probability that the company receives exactly 17 claims between 08:00 and 16:00?

Answer 1

Let $X=$ the number of claims received: $X\sim Po(\lambda t).$

Given $\lambda=6,t=\dfrac{16-8}{16-14}=4$

$$P(X=7)=\dfrac{e^{-6\cdot 4}(6\cdot 4)^{17}}{{17}!}\approx0.030864$$