Assume that a certain tire manufacturer produces …….

Question

Assume that a certain tire manufacturer produces a new tire. Tests show that the number of miles these tires last before blow-out seems to have a normal distribution with a mean of 60,000 miles and a standard deviation of 4,000 miles.

(a) Do you think they should warrant their tires for 60,000 miles? Briefly explain why or why not.

(b) If they warrant their tires for 52,000 miles, what percentage of the tires would they expect to blow out while still under warranty?

(c) How many miles should they warrant their tires for if they are willing to pay-off on 5% of their tires?

Answer 1

Hi Lilly!

For part a, they should not warrant their tires as there is a 50% chance (as 60,000 miles is the mean) that they have to replace the tire due to it blowing out - they would suffer as a business.

B. Using the equation Probability of z < ((Amount we are looking for - Mean)/Standard deviation). We get 52,000 - 60,000 / 4,000 = z < -2. Using the z-score table we get a percentage of 2.28%.

C. We need to find what number of miles for the tires is the threshold for 5%. We use the z-score for 5% while is -1.645 (for a left tail) and make it equal to the same equation as above but with different numbers. Thus we get: -1.645 = (x - 60,000) / 4,000 = 53,420 miles.

Hope this helps! Please let me know if you have any other questions.