To estimate the average number of miles tires at RoadStar will last, a random sample of 64 tires is tested. If the sample mean produced is 35,000 miles and the population standard deviation is 5000 miles, then a 90% confidence interval is ______.

A. 30,000 < m < 40,000
B. 26,775 < m < 43,225
C. 33,972 < m < 36,028

Correct Answer: C

For a 90% confidence interval, we find z(0.05), the cutoff for the top 5% of the normal distribution. Looking up 0.95 in the middle of the table, the reading to the row/column values, we get 1.645. Working with the formula for E (see top right) we get E = 1028. So, the 90% confidence interval is 35.000 - 1028 < m < 35,000 + 1028 or 33,972 < m < 36,028.