Question: The Summa is a new sports car. An extended transmission warranty is available for $1500 that will replace or repair the transmission if it fails during the first 65,000 miles. The normal warranty period is for 24,000 miles. A random sample of eight Summas were driven under a variety of conditions until the transmission failed. The mileage at the time of transmission failure was recorded. These data are (in miles) Assume mileages are normally distributed.

75,436 80,212 42,316 25,415

61,335 50,720 52,318 66,143

The following table provides sample information for the above data.

Find a 90% confidence interval for mileage at the time of transmission.