A certain brand of automobile tire has a mean life span of 36,000 miles and a standard deviation of 2,150 miles.? (Assume the life spans of the tires have a? bell-shaped distribution.)

?(a) The life spans of three randomly selected tires are 33,000 ?miles, 37,000 ?miles, 31,000 miles. Find the? z-score that corresponds to each life span.

For the life span of 33,000 ?miles, z-score is

For the life span of 37,000 ?miles, z-score is

For the life span of 31,000 ?miles, z-score is

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

b) The life spans of three randomly selected tires are 31,700 ?miles, 40,300 ?miles, and 36,000 miles. Using the empirical? rule, find the percentile that corresponds to each life span.

The life span 31,700 miles corresponds to the _ percentile.

The life span 40,300 miles corresponds to the _ percentile.

The life span 36,000 miles corresponds to the _ percentile.