Suppose storms hit A as a Poisson process with an average of 3 per year. Suppose each time a storm hits, there is a 0.4% chance that school is closed. Determine the time by which school has a 50% chance of closed.
my orginal though is that we could calculate E and V by using thining Poisson. But my problem here is that it does not follow to normal distribution then i could not use pnorm to calculate and find out the time
Take $C(t)$ as the number of times the school has closed on $[0,t)$ where $t$ is in years. Then $C(t)\sim \text{Poisson}\Big({12t \over 1000}\Big)$ and $$P(C(t)\geq 1)=1-P(C(t)=0)=1- \exp\Big\{-\frac{12 t}{1000}\Big\}$$ So $P(C(t)\geq 1)=0.5$ implies $t=\frac{1000 \ln(2)}{12}\approx 57.8$ years.