A certain brand of automobile tire has a mean life span of 38,000 miles and a st

Question

A certain brand of automobile tire has a mean life span of 38,000 miles and a standard deviation of 2,400 miles. (Assume the life spans of the tires have a bell-shaped distribution.) (a) The life spans of three randomly selected tires are 33,000 miles, 37,000 miles, and 32,000 miles. Find the z-score that corresponds to each life span. For the life span of 33,000 miles, z-score is (Round to the nearest hundredth as needed.) For the life span of 37,000 miles, z-score is (Round to the nearest hundredth as needed.) For the life span of 32,000 miles, z-score is (Round to the nearest hundredth as needed.) According to the z-scores, would the life spans of any of these tires be considered unusual? O No O Yes (b) The life spans of three randomly selected tires are 33,200 miles, 42,800 miles, and 38,000 miles. Using the empirical rule, find the percentile that corresponds to each life span The life span 33,200 miles corresponds to the th percentile. The life span 42,800 miles corresponds to theth percentile The life span 38,000 miles corresponds to the th percentile.

Explanation / Answer

a)

for 33000 ; z score = -2.08

for 37000 ; z score =-0.42

for 32000 ; z score =-2.5

b)

from empriical rule: life spam 33200 corresponds to 2.5th percentile

life spam 42800 corresponds to 97.5th percentile

life spam 38000 corresponds to 50th percentile

for normal distribution z score =(X-)/ here mean=       = 38000.000 std deviation   == 2400.00

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.