Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Tests revealed that the tire's mileage is normally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 5% of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce?
A)44,518
B)32,960
C)49,621
D)40,922

Question

Quizplus · Accepted Answer

To ensure no more than 5% of the tires will have to be replaced, the manufacturer should set the guaranteed mileage at the 5th percentile of the normal distribution. Using the Z-score formula, Z = (X - μ) / σ, where Z is the Z-score corresponding to the 5th percentile, X is the mileage, μ is the mean, and σ is the standard deviation. The Z-score for the 5th percentile is approximately -1.645. Plugging in the values: -1.645 = (X - 47,900) / 2,050. Solving for X gives X ≈ 44,518 miles.

Suppose a Tire Manufacturer Wants to Set a Mileage Guarantee