You work in marketing for a company that produces work boots.Quality control has sent you a memo detailing the length of timebefore the boots wear out under heavy use. They found thatthe average length of time until the boots wear out is normallydistributed with a mean of 208 days and a standard deviation of 14days. You would like to run a marketing campaign stating thatthe boots will last more than 8 months (240 days).

What is the probability that this marketing claim is true (e.g.,what is the probability that the length of time until the bootswear out is more than 240 days)?

Based on your answer to part a, would you feel comfortablerunning the marketing campaign? Why or why not?

what is the probability that a randomly selected pair of bootsis “below average” with respect to the length of time before theywear out under heavy use (e.g., the time until they wear out isless than 208 days)?

What is the probability that more than half of the customers hadboots that were below average (lasted less than 208 days)?