The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.What percentage of tires will have a life of 34,000 to 46,000 miles?
A) 38.49%
B) 76.98%
C) 50%
D) 88.49%

Question

Quizplus · Accepted Answer

To find the percentage of tires that will have a life of 34,000 to 46,000 miles, we need to calculate the area under the normal distribution curve between these two values. We can do this by standardizing the values using the formula:
z = (x - mu) / sigma
where x is the value we want to standardize, mu is the mean, and sigma is the standard deviation. 
For x = 34,000:
z = (34,000 - 40,000) / 5,000 = -1.2
For x = 46,000:
z = (46,000 - 40,000) / 5,000 = 1.2
Using a standard normal distribution table or calculator, we can find that the area between z = -1.2 and z = 1.2 is approximately 0.7698 or 76.98%. Therefore, the percentage of tires that will have a life of 34,000 to 46,000 miles is 76.98%.

The Life Expectancy of a Particular Brand of Tire Is