Question

a certain brand of automobile tire has a mean life span of 38,000 miles and a standard deviation of 2,450 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 31,000 miles. find the z - score that corresponds to each life span. for the life span of 34,000 miles, z - score is \\(\square\\). (round to the nearest hundredth as needed.)

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the dataset, $\mu$ is the mean, and $\sigma$ is the standard deviation.
Here, $\mu = 38000$ miles, $\sigma=2450$ miles, and for the first value, $x = 34000$ miles.

Step2: Substitute values into formula

Substitute $x = 34000$, $\mu=38000$, and $\sigma = 2450$ into the z - score formula:
$z=\frac{34000 - 38000}{2450}=\frac{- 4000}{2450}\approx - 1.63$

Answer:

-1.63