Show your calculation in detail explaining each step. Make sure to show the critical value and the statistical table, which points to the value you used for the answer as well as other values to have come to an answer.

1. A car dealer recommends that transmissions be serviced at 30000 miles. To see whether her customers are adhering to this recommendation, the dealer selects a sample of 40 customers and finds that the average mileage of the automobiles serviced is 30456. The standard deviation of the sample is 1684 miles. By using P-value method, and = 0.01, determine whether the owners are having their transmissions serviced at 30000 miles. (Answer: Reject H0 )
2. Explain in detail how you picked the P-value from the table AND WHY USED THE DISTRIBUTION THAT YOU USED FOR YOUR ANSWER. FOR EXAMPLE, IF YOU USED Z-DISTRIBUTION, YOU MUST EXPLAIN WHY YOU CHOSE IT OVER T-DISTRIBUTION.