Experts are full of valuable knowledge and are ready to help with any question. Credentials confirmed by a Fortune 500 verification firm.

Get a Professional Answer

Via email, text message, or notification as you wait on our site. Ask follow up questions if you need to.

100% Satisfaction Guarantee

Rate the answer you receive.

Ask mathsmart Your Own Question

mathsmart, Tutor

Category: Homework

Satisfied Customers: 909

Experience: BA in Math. Over six years experience in teaching and tutoring math and standardized test prep.

1883086

Type Your Homework Question Here...

mathsmart is online now

The tread life of a particular brand of tire is a random ...

Resolved Question:

The tread life of a particular brand of tire is a random variable best descrided by a normal distribution with a mean of 60,000 miles and standard deviation of 12,000 miles. What is the probability a particular tire of this brand will last between 62,160 and 62,520 miles?

You need to find the Z-scores corresponding to 62,160 and 62,520

Z = (x - μ)/σ

So the Z-score for 62,160 is:

(62,160 - 60,000)/12,000 = .18

The Z-score for 62,520 is:

(62,520 - 60,000)/12,000 = .21

Using a calculator the area under the curve corresponding to the interval of .18 to .21 is approximately .0117, so the probability is approximately 1.17%.

mathsmart and 4 other Homework Specialists are ready to help you

b.If the manufacturer gaurantees the tread life of this brand will last between 58,620 miles, what proportion of the tires will need to be replaced under warranty?

c. If the manufacturer sells 500,000 of these tire, how many would you expect to need replaced under warranty?