A certain brand of automobile tire has a mean life span of 38,000 miles and a standard deviation of 2,400 miles. (Assume the life spans of the tires have a bell-shaped distribution.)

(a) The life spans of three randomly selected tires are 35,000 miles, 37,000 miles, and

32,000 miles. Find the z-score that corresponds to each life span.

For the life span of 35,000 miles, z-score is___

(Round to the nearest hundredth as needed.)

Part 2 For the life span of 37,000 miles, z-score is_____

(Round to the nearest hundredth as needed.)

Part 3For the life span of 32,000 miles, z-score is____

(Round to the nearest hundredth as needed.)

According to the z-scores, would the life spans of any of these tires be considered unusual?

No or Yes

(b) The life spans of three randomly selected tires are 33,200 miles, 42,800 miles, and

38,000 miles. Using the empirical rule, find the percentile that corresponds to each life span.

The life span 33,200 miles corresponds to a percentile of____

The life span 42,800 miles corresponds to a percentile of_____

The life span 38,000 miles corresponds to a percentile of_____

(Round to the nearest whole number as needed.)