Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 miles and a standard deviation of 5000 miles.What is the probability that a randomly selected tire of this brand has a life of at least 50,000 miles?
A)0.0228
B)0.9772
C)0.5000
D)0.4772
E)1.0000

Question

Quizplus · Accepted Answer

To find the probability that a tire has a life of at least 50,000 miles, we calculate the Z-score for 50,000 miles using the formula Z = (X - μ) / σ, where X is the value of interest (50,000 miles), μ is the mean (40,000 miles), and σ is the standard deviation (5,000 miles). Thus, Z = (50,000 - 40,000) / 5,000 = 2. The probability of a Z-score being greater than 2 (to the right of 2 on the standard normal distribution) is approximately 0.0228.

Sure Stone Tire Company Has Established That the Useful Life