Question

It is assumed that the number of claims arriving at an insurance company per working day has a mean of 40 and a standard deviation of 12. A survey was conducted over 50 working days. Find the probability that the sample mean number of claims arriving per working day was less than 35.

Answer 1

$$P(X<35)=P(Z<\dfrac{35-40}{12/\sqrt{50}})$$

$$\approx P(Z<-2.9463)\approx0.0016$$