Question

The mean number of houses sold by a real estate agent per week is 2. Find the

probability that over the next 6 weeks, the real-estate agent sells between 5 and

12 houses (both inclusive).

Answer 1

This is a Poisson distribution with $\mu=2*6=12.$

$P(5\le X\le12)=e^{-12}(\frac{12^5}{5!}+\frac{12^6}{6!}+\frac{12^7}{7!}+\frac{12^8}{8!}+\frac{12^9}{9!}+\frac{12^{10}}{10!}+\frac{12^{11}}{11!}+\frac{12^{12}}{12!})=0.5684.$