In a city there is 1000 houses. We know that each house has 1/2 chance to not have any mouse. (So with 1/2 chance, it has 1 or more mice). A person gets 1$ for every ten mice he catches.
a) Find the probability that after checking all of the houses, he gets more than 2$.
b) If we denote average mice he catches in a house by $M$, How many houses he should search such that $P(0.3\leq M \leq 0.7)\geq0.9$
At first I thought we have a binomial distribution but I found out that we don't know what is the distribution exactly because we want number of mouses and not if they exist or not. The question is actually from a quiz designed for central limit theorem but we don't know average nor the variance of distribution to use CLT.
What should I do?