UO Luxury is a residential rental company that advertises that the average cost of a rental for undergraduate students at the University of Oregon is $535 with a standard deviation of $90. (Let us assume the rents are approximately Normally distributed.) The Department of Consumer Protection will investigate the company if, when they choose a sample of students, they found that the average rental cost for those students is $600 or more.
(a) Assuming that the company is advertising truthfully, what is the probability that the company will be investigated if the Department of Consumer Protection only samples one client?
(b) Assuming that the company is advertising truthfully, what is the probability that the company will be investigated if the Department of Consumer Protection samples 5 clients?
(c) (Assuming that the company is advertising truthfully, what is the probability that the company will be investigated if the Department of Consumer Protection samples 20 clients?