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 -3.41.
(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

Explanation:

Identify given parameters

Using the Z-Score Calculation knowledge point

$$
LATEXBLOCK0
$$

Calculate z-scores

Using the Z-Score Calculation knowledge point

$$
LATEXBLOCK1
$$

Interpret unusual values

Using the Z-Score Interpretation knowledge point

$$
LATEXBLOCK2
$$

Answer:

• No
• Yes (Correct answer)