Question

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 20,138 miles, with a variance of 10,304,100. What is the probability that the sample mean would differ from the population mean by less than 236 miles in a sample of 171 tires if the manager is correct? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 20138

standard deviation = = 3210

= / n = 3210 / 171 = 245.4748

= P[(-236) /245.4748 < ( - ) / < (236) / 245.4748)]

= P(-0.96 < Z < 0.96)

= P(Z < 0.96) - P(Z < -0.96)

= 0.8315 - 0.1685

= 0.6630

Probability = 0.6630