Find and Interpret the Area under a Normal Curve
-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 1300 miles. What is the probability a particular tire of this brand will last longer than 58,700 miles
A) 0.8413
B) 0.1587
C) 0.2266
D) 0.7266

Question

Quizplus · Accepted Answer

To find the probability that a tire will last longer than 58,700 miles, we calculate the z-score and then use the standard normal distribution table or a calculator. The z-score is calculated as $z = \frac{X - \mu}{\sigma}$, where $X$ is the value in question (58,700 miles), $\mu$ is the mean (60,000 miles), and $\sigma$ is the standard deviation (1300 miles). Plugging in the values, we get $z = \frac{58700 - 60000}{1300} = -1$. Looking up the z-score of -1 in the standard normal distribution table or using a calculator, we find that the area to the left of z = -1 is approximately 0.1587. Since we are interested in the probability of lasting longer than 58,700 miles, we look for the area to the right, which is $1 - 0.1587 = 0.8413$.

Find and Interpret the Area Under a Normal Curve