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 of at most 30,000 miles?
A)0.5000
B)0.4772
C)0.0228
D)0.9772
E)1.0000

Question

Quizplus · Accepted Answer

To find the probability that a tire has a life of at most 30,000 miles, we calculate the Z-score and then look up the corresponding probability in a standard normal distribution table. The Z-score is calculated as $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (30,000 miles), $\mu$ is the mean (40,000 miles), and $\sigma$ is the standard deviation (5,000 miles). Plugging in the values, we get $Z = \frac{30,000 - 40,000}{5,000} = -2$. Looking up the Z-score of -2 in a standard normal distribution table gives a probability of approximately 0.0228.

Sure Stone Tire Company Has Established That the Useful Life