The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean $\mu = 40$ and standard deviation $\sigma = 7$ . What proportion of tires have lifetimes of less than 42 Thousand miles?
A) 0.3070
B) 0.6930
C) 0.3859
D) 0.6141

Question

Quizplus · Accepted Answer

To find the proportion of tires with lifetimes less than 42, we calculate the z-score: $ z = \frac{42 - 40}{7} = \frac{2}{7} \approx 0.2857 $. Using the standard normal distribution table, the cumulative probability for $ z = 0.2857 $ is approximately 0.6141.

The Lifetime of a Certain Type of Automobile Tire (In μ=40\mu = 40μ=40

The Lifetime of a Certain Type of Automobile Tire (In $\mu = 40$