PLEASE help me with a,b, c and d! thanks!

(28 points) You own many taxi cabs and hire people to drive them for you. There are two types of drivers, hard working drivers and lazy drivers. Every day the amount that each type of driver earns is a normal random variable. The table below summarizes their distributions: Driver type [J a Hardworking 400 100 Lazy 350 100 (a) What is the probability of earning less than $300 in a day for a hard-working driver? (b) Suppose you have 300 hard-working drivers and 100 lazy drivers. If a randomly chosen driver makes less than $300 in a day, what is the probability he was a hard-working driver? (0) Suppose you decide to record all taxi drivers' earnings for four days and then nd the four-day average for each driver. All of the drivers with an average earnings of less than $300 will be given a warning that you think they are being lazy. Find the probability that a hardworking driver will receive a warning. ((1) Too many hard-working drivers are unfairly receiving warnings. You decide that you want to observe the drivers for long enough that hardworking drivers have only a 1/200 chance of receiving a warning. If H is average earnings of a hard working driver over n different days H1+H2+H3+...Hn H\" = It Find 72 such that PU?\"