Find the Value of a Normal Random Variable
-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 2900 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty
A) 54,925 mi
B) 65,075 mi
C) 57,100 mi
D) 62,900 mi

Question

Quizplus · Accepted Answer

To find the warranty mileage for which 96% of the tires will outlast, we need to find the 4th percentile of the normal distribution. Using the Z-table, the Z-score for 4% in the left tail is approximately -1.75. Using the formula: X = μ + Zσ, we get X = 60000 + (-1.75)(2900) = 54,925 miles.