Question

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, 38,000 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. the life span 38,000 miles corresponds to a percentile of. the life span 34,000 miles corresponds to a percentile of. (round to the nearest whole number as needed.)

Explanation:

Step1: Recall the empirical - rule for z - scores and percentiles

The empirical rule states that for a normal distribution: about 68% of the data lies within z = - 1 and z = 1, about 95% lies within z=-2 and z = 2, and about 99.7% lies within z=-3 and z = 3. The area under the standard - normal curve to the left of z gives the percentile.

Step2: Find the percentile for a z - score of 1.67

Using a standard normal distribution table (or z - table), the area to the left of z = 1.67 is approximately 0.9525. So the percentile is 95 (rounded to the nearest whole number).

Step3: Find the percentile for a z - score of - 1.25

Using the z - table, the area to the left of z=-1.25 is approximately 0.1056. So the percentile is 11 (rounded to the nearest whole number).

Step4: Assume the third z - score is 0 (since not given, assume it's the mean for simplicity)

The area to the left of z = 0 is 0.5. So the percentile is 50.

Answer:

The life - span of 29200 miles corresponds to a percentile of 11.
The life - span of 38800 miles corresponds to a percentile of 95.
The life - span of 34000 miles corresponds to a percentile of 50.