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 $\mu = 40$ and standard deviation $\sigma = 6$ . What Proportion of tires have lifetimes greater than 32 thousand miles?
A) 0.9544
B) 0.9088
C) 0.0456
D) 0.0912

Question

Quizplus · Accepted Answer

To solve the problem using technology, we can use a standard normal distribution table or calculator. First, we need to standardize the value of 32 using the formula:

z = (x - mu) / sigma

where x is the value we are interested in (32), mu is the mean (40), and sigma is the standard deviation (6). Thus:

z = (32 - 40) / 6 = -1.33

Next, we look up the proportion of the standard normal distribution that is greater than -1.33. Using a table or calculator, we find this to be approximately 0.9088. Therefore, the proportion of tires with lifetimes greater than 32 thousand miles is approximately 0.9088 or 90.88%. The closest choice to this answer is B, with 0.9088 being the correct value rounded to four decimal places.

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