The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean $\mu = 43$ and standard deviation $\sigma = 5$ . What proportion of tires have lifetimes between 40 and 50 thousand miles?
A) 0.6450
B) 2.0000
C) 0.3550
D) 1.1935

Question

Quizplus · Accepted Answer

To find the proportion of tires with lifetimes between 40 and 50 thousand miles, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$. For X = 40, $Z = \frac{40 - 43}{5} = -0.6$, and for X = 50, $Z = \frac{50 - 43}{5} = 1.4$. Looking these Z-scores up in the standard normal distribution table gives us the probabilities of 0.7257 and 0.0803, respectively. Subtracting these gives us the proportion of tires in this range: 0.7257 - 0.0803 = 0.6454, which is approximately 0.6450.

The Lifetime of a Certain Type of Automobile Tire (In μ=43\mu = 43μ=43

The Lifetime of a Certain Type of Automobile Tire (In $\mu = 43$