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

(b) the life spans of three randomly selected tires are 35,950 miles, 40,050 miles, and 38,000 miles. using the empirical rule, find the percentile that corresponds to each life span.

the life span 35,950 miles corresponds to a percentile of
the life span 40,050 miles corresponds to a percentile of
the life span 38,000 miles corresponds to a percentile of
(round to the nearest whole number as needed.)

Explanation:

Identify the given parameters

Using the Z-Score Calculation knowledge point

$$
LATEXBLOCK0
$$

Calculate standard deviations from the mean

Using the Empirical Rule Percentiles knowledge point

$$
LATEXBLOCK1
$$

Determine the percentile for each z-score

Using the Empirical Rule Percentiles knowledge point

$$
LATEXBLOCK2
$$

Answer:

The life span 35,950 miles corresponds to a percentile of <blank>16</blank>
The life span 40,050 miles corresponds to a percentile of <blank>84</blank>
The life span 38,000 miles corresponds to a percentile of <blank>50</blank>