A certain brand of automobile tire has a mean life span of 36,000 miles and a standard deviation of 2,250 miles. (Assume the life spans of the tires have a bell-shaped distribution.)
(a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 32,000 miles. Find the z-score that corresponds to each life span.
For the life span of 34,000 miles, z-score is ___________(Round to the nearest hundredth as needed.)
For the life span of 37,000 miles, z-score is _________(Round to the nearest hundredth as needed.)
For 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?
yes or no? _________
(b) The life spans of three randomly selected tires are 31,500 miles, 40,500 miles, and 36,000 miles. Using the empirical rule, find the percentile that corresponds to each life span.
The life span 31,500 miles corresponds to the ___________th percentile.
The life span 40,500 miles corresponds to the ________th percentile.
The life span 36,000 miles corresponds to the ___________th percentile.