Use technology to solve the following problem: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean $\mu = 44$ and standard deviation $\sigma = 4$ . What Proportion of tires have lifetimes of less than 49 thousand miles?
A) 0.1056
B) 0.4472
C) 0.8944
D) 0.5528

Question

Quizplus · Accepted Answer

To find the proportion of tires with lifetimes less than 49 thousand miles, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X = 49$, $\mu = 44$, and $\sigma = 4$. Plugging in the values, we get $Z = \frac{49 - 44}{4} = 1.25$. Looking up 1.25 in the Z-table or using a normal distribution calculator gives us a proportion of approximately 0.8944, indicating that about 89.44% of the tires have lifetimes of less than 49 thousand miles.

Use Technology to Solve the Following Problem: the Lifetime of a Certain