36.A manufacturer claims that the life span of its tires is 47,000 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 46,774 miles.Assume =700. Complete parts(a) through(c).

(a) Assuming themanufacturer's claim iscorrect, what is the probability that the mean of the sample is 46,774 miles orless?_____________

(Round to four decimal places asneeded.)