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 between 30,000 and 50,000 miles?
A) 0.5000
B) 0.4772
C) 0.9544
D) 0.9772
E) 1.0000

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected tire of this brand has a life between 30,000 and 50,000 miles, we need to calculate the z-scores for both values first:

z1 = (30,000 - 40,000) / 5000 = -2
z2 = (50,000 - 40,000) / 5000 = 2

Then, we can use a standard normal distribution table or calculator to find the area under the curve between these z-scores:

P(-2 < Z < 2) = 0.9544

Therefore, the probability that a randomly selected tire of this brand has a life between 30,000 and 50,000 miles is 0.9544, which corresponds to answer choice C.

Sure Stone Tire Company Has Established That the Useful Life