The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.What is the probability that a randomly selected tire will have a life of at least 30,000 miles?
A) 0.4772
B) 0.9772
C) 0.0228
D) 0.5000

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected tire will have a life of at least 30,000 miles, we need to find the area under the normal distribution curve to the right of 30,000 miles. 
Using the standard normal distribution formula, Z= (x - μ) / σ, we get Z = (30,000 - 40,000) / 5,000 = -2. 
Looking up the area under the standard normal distribution curve for Z = -2, we find that it is 0.0228. 
Therefore, the probability that a randomly selected tire will have a life of at least 30,000 miles is 1 - 0.0228 = 0.9772 or approximately 97.72%. 
Thus, the best choice is B.

The Life Expectancy of a Particular Brand of Tire Is