A manufacturer claims that the life span of its tires is 51,000 miles. You work for a consumer protection agency and you are testing these tires.

A manufacturer claims that the life span of its tires is 51,000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The mean life span is 50,748 miles. Assume σ=800. Complete parts​ (a) through​ (c). ​(a) Assuming the​ manufacturer's claim is​ correct, what is the probability that the mean of the sample is 50,748 miles or​ less? b) using your answer from part a what do you think is the manufacturers claim? c) would it be unusual to have an individual tire with a lifespan of 50,748 miles? why or why not?