Solve the problem.
-The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1200 miles. What warranty should the company use if they
Want 96% of the tires to outlast the warranty?
A) 62,100 mi
B) 61,200 mi
C) 57,900 mi
D) 58,800 mi

Question

Quizplus · Accepted Answer

To ensure 96% of the tires outlast the warranty, the warranty should be set at a point below the mean where 4% of the distribution lies to the left (since 100% - 96% = 4%). In a normal distribution, a Z-score of approximately -2 corresponds to the 2.5th percentile, but since we're looking for the 4th percentile, the Z-score is slightly higher than -2. Using the Z-score formula: Z = (X - μ) / σ, where X is the value we're looking for, μ is the mean, and σ is the standard deviation. Rearranging the formula to solve for X gives us X = Zσ + μ. The Z-score for 4% is approximately -1.75 (since it's slightly above the -2 standard deviations for the 2.5th percentile). Plugging in the values gives us X = -1.75(1200) + 60,000 = -2100 + 60,000 = 57,900 miles. Therefore, the warranty should be set at 57,900 miles to ensure that 96% of the tires outlast the warranty.

Solve the Problem. -The Tread Life of a Particular Brand of Tire Is