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.Which probability most closely reflects that a randomly selected tire of this brand has a life between 30,000 and 50,000 miles?
A)0.5000
B)0.4772
C)0.9544
D)0.9772
E)1.0000

Question

Quizplus · Accepted Answer

To find the probability that a tire has a life between 30,000 and 50,000 miles, we calculate the Z-scores for both 30,000 and 50,000 miles and then find the corresponding probabilities from the standard normal distribution. The Z-score is calculated as $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For 30,000 miles, $Z = \frac{30,000 - 40,000}{5,000} = -2$, and for 50,000 miles, $Z = \frac{50,000 - 40,000}{5,000} = 2$. Looking up these Z-scores in a standard normal distribution table or using a calculator, the area between $Z = -2$ and $Z = 2$ is approximately 0.9544, which represents the probability that a tire will last between 30,000 and 50,000 miles.

Sure Stone Tire Company Has Established That the Useful Life