Question

question 7
the lifetime in miles for a certain brand of tire is normally distributed with a mean of 22,000 miles and a standard deviation of 3,100 miles the tire manufacturer wants to offer a money - back guarantee so that no more than 3% of tires will qualify for a refund. what is the minimum number of miles the manufacturer should guarantee that the tires will last?
a. 27,828 miles
b. 15,800 miles
c. 25,007 miles
d. 16,172 miles

Explanation:

Step1: Find z - score for 3%

The z - score corresponding to a left - tail area of 0.03 is approximately $z=- 1.88$.

Step2: Use z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$. Rearranging for $x$ gives $x=\mu + z\sigma$. Substitute $\mu = 22000$, $z=-1.88$ and $\sigma = 3100$. So $x=22000+( - 1.88)\times3100=22000 - 5828=16172$.

Answer:

D. 16,172 miles