The tread life of a particular brand of tire is a random variable best described by a normal distribution with amean of 60,000 miles and a standard deviation of 2900 miles. What is the probability a certain tire of this brandwill last between 53,910 miles and 54,780 miles?
A) 0.0180
B) 0.9813
C) 0.4920
D) 0.4649

Question

Quizplus · Accepted Answer

To find the probability that the tire lasts between 53,910 miles and 54,780 miles, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For 53,910 miles, $Z = \frac{53910 - 60000}{2900} = -2.10$, and for 54,780 miles, $Z = \frac{54780 - 60000}{2900} = -1.79$. Looking these Z-scores up in a standard normal distribution table or using a calculator, the probability of being between these Z-scores is approximately 0.0180.

The Tread Life of a Particular Brand of Tire Is