$3.$ Historically, the number of sales made at a convenience store in the time period between $1$ am and $5$ am is $25.$

a$.$ What is the probability that on a randomly selected night, you would observe exactly $22$ customers? $0\mathrm{.}062(6\mathrm{.}2\%)$

b$.$Assume the average purchase is $$8$ per customer, and your only expenses are fixed costs of $$4$ per hour and the wages of one employee at $$15$ per hour. How many customers do you need to break even $($i$.$e$.$ net profit of $=0$ for that single $4$ hour period$)?$ Now estimate the probability of breaking even or losing money $($i$.$e$.$ net profit of $<=0$ for that single $4$ hour period$).$ Show your calculations$/$reasoning$.$ Remember that you lose money with $<=$ your break$-$even number of customers, not just $=$ to that number.