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 1900 miles. What is the
Probability a certain tire of this brand will last between 56,010 miles and 56,580 miles?
A).0180
B).9813
C).4649
D).4920

Question

Quizplus · Accepted Answer

To find the probability that the tire will last between 56,010 miles and 56,580 miles, we first convert these values to z-scores using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For 56,010 miles: $z_1 = \frac{(56010 - 60000)}{1900} = -2.1$, and for 56,580 miles: $z_2 = \frac{(56580 - 60000)}{1900} = -1.8$. Looking these z-scores up in a standard normal distribution table or using a calculator, we find the probabilities corresponding to these z-scores and subtract the smaller from the larger to find the probability of a tire lasting between these mileages. The probability corresponding to this range is approximately 0.0180, making option A correct.

The Tread Life of a Particular Brand of Tire Is