Answer to Question #45577 in Statistics and Probability for Monam Khan

Question

General Co. has designed a new tire, and they don’t know what the average amount of tread life is going to be. The tread life is normally distributed with a standard deviation of 295.5 kilometers.
i) If the company samples 800 tires and records their tread life, what is the probability the sample mean is between the true mean and 350 kilometers over the true mean?
ii) How large a sample must be taken to be 95 percent sure the sample mean will be within 150 kilometers of the true mean?