Question

a certain brand of automobile tire has a mean life span of 38,000 miles and a standard deviation of 2,050 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 -1.95
(round to the nearest hundredth as needed.)

for the life span of 37,000 miles, z-score is -0.49
(round to the nearest hundredth as needed.)

for the life span of 31,000 miles, z-score is
(round to the nearest hundredth as needed.)

Explanation:

Identify given parameters

Using the Z-Score Calculation knowledge point

$$
LATEXBLOCK0
$$

Calculate the z-score

Using the Z-Score Calculation knowledge point

$$
LATEXBLOCK1
$$

Round to the nearest hundredth

Using the Z-Score Calculation knowledge point

$$ z \approx -3.41 $$

Answer:

For the life span of 31,000 miles, z-score is <blank>-3.41</blank>