Question

(a) the life spans of three randomly selected tires are 33,000 miles, 38,000 miles, and 31,000 miles. find the z - score that corresponds to each life span.
for the life span of 33,000 miles, z - score is - 0.42
(round to the nearest hundredth as needed.)
for the life span of 38,000 miles, z - score is 1.67
(round to the nearest hundredth as needed.)
for the life span of 31,000 miles, z - score is - 1.25
(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
yes
(b) the life spans of three randomly selected tires are 29,200 miles, 38,800 miles, and 34,000 miles. using the empirical rule, find the percentile that corresponds to each life span.
the life span 29,200 miles corresponds to a percentile of 3
the life span 38,800 miles corresponds to a percentile of 98
the life span 34,000 miles corresponds to a percentile of 50
(round to the nearest whole number as needed.)

Explanation:

Step1: Recall the rule for unusual z - scores

A z - score is considered unusual if \(|z|> 2\).

Step2: Check each z - score

For \(z=-0.42\), \(|z| = 0.42<2\).
For \(z = 1.67\), \(|z|=1.67<2\).
For \(z=-1.25\), \(|z| = 1.25<2\).

Answer:

No