A prototype automotive tire has a design life of 38,500 miles with a standard deviation of 2,500 miles. The manufacturer tests 60 such tires. On the assumption that the actual population mean is 38,500 miles and the actual population standard deviation is 2,500 miles, find the probability that the sample mean will be less than 36,000 miles. Assume that the distribution of lifetimes of such tires is normal.   Let X = number of miles on a single tire. Write the question above in terms of this variable X.       Using the software tool above, find the probability stated on part (a)               Using the software tool above, graph the probability of stated on part (b)

DATAfile: Costco You may need to use the appropriate technology to answer this question. Consumer Reports uses a 100-point customer satisfaction score to rate the nation's major chain stores. Assume that from past experience with the satisfaction rating score, a population standard deviation of ? = 13 is expected. In 2012, Costco, with its 432 warehouses in 40 states, was the only chain store to earn an outstanding rating for overall quality. A sample of 15 Costco customer satisfaction scores follows. 95 90 83 75 95 98 80 83 82 93 86 80 94 64 62 (a) What is the sample mean customer satisfaction score for Costco?   (b) What is the sample variance? (Round your answer to two decimal places.)   (c) What is the sample standard deviation? (Round your answer to two decimal places.)   (d) Construct a hypothesis test to determine whether the population standard deviation of ? = 13 should be rejected for Costco. With a 0.05 level of significance, what is your conclusion?…

please add excel formulas too.

High-rent district: The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2550. Assume the standard deviation is $485. A real estate firm samples 85 apartments. Use Excel.