Question

A tire manufacturer states that a certain type of tire has a mean lifetime of 60,000 miles. Suppose lifetimes are normally distributed with standard deviation ơ = 3,500 miles.

- Find the probability that if you buy one such tire, it will last only 57,000 or fewer miles. If you had this experience, is it particularly strong evidence that the tire is not as good as claimed?
- The tire manufacturer offers a money back guarantee if the tire needs to be replaced before 65,000 miles. What is the probability a customer will get their money back?
- The tire manufacturer only wants a return rate of 10%. At what mileage should they then offer a guarantee?

Answer #1

Define the standard random variable Z as Where X denotes lifetime

a) Using normal table we have

b) Required probability is

c) Let be the mileage such that

Then we know from normal table that

Hence

So the mileage should be 64,480

Tire lifetimes: The lifetime of a certain type of automobile
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40 and a standard deviation of 5.
(a) Find the 14th percentile of tire lifetimes.
(b) Find the 66th percentile of tire lifetimes.
(c) Find the third quartile of the tire lifetimes.
(d) The tire company wants to guarantee that its tires will last
at least a certain number of miles. What number of miles (in
thousands) should the...

Tire lifetimes: The lifetime of a certain type
of automobile tire (in thousands of miles) is normally distributed
with mean
=μ41
and a standard deviation
=σ4
.
(a) Find the
13th
percentile of tire lifetimes.
(b) Find the
65th
percentile of tire lifetimes.
(c) Find the first quartile of the tire lifetimes.
(d) The tire company wants to guarantee that its tires will last
at least a certain number of miles. What number of miles (in
thousands) should the company...

. Grear Tire Company has produced a new tire with an estimated
mean lifetime mileage of 36,500 miles. Management also believes
that the standard deviation is 5,000 miles and that tire mileage is
normally distributed. To promote the new tire, Grear has offered to
refund some money if the tire fails to reach 30,000 miles before
the tire needs to be replaced. Specifically, for tires with a
lifetime below 30,000 miles, Grear will refund a customer $1 per
100 miles...

Grear Tire Company has produced a new tire with an estimated
mean lifetime mileage of 36,500 miles. Management also believes
that the standard deviation is 5,000 miles and that tire mileage is
normally distributed. To promote the new tire, Grear has offered to
refund some money if the tire fails to reach 30,000 miles before
the tire needs to be replaced. Specifically, for tires with a
lifetime below 30,000 miles, Grear will refund a customer $1 per
100 miles short...

Grear Tire Company has produced a new tire with an estimated
mean lifetime mileage of 36,500 miles. Management also believes
that the standard deviation is 5,000 miles and that tire mileage is
normally distributed. To promote the new tire, Grear has offered to
refund some money if the tire fails to reach 30,000 miles before
the tire needs to be replaced. Specifically, for tires with a
lifetime below 30,000 miles, Grear will refund a customer $1 per
100 miles short...

Grear Tire Company has produced a new tire with an estimated
mean lifetime mileage of 36,500 miles. Management also believes
that the standard deviation is 5000 miles and that tire mileage is
normally distributed. To promote the new tire, Grear has offered to
refund some money if the tire fails to reach 30,000 miles before
the tire needs to be replaced. Specifically, for tires with a
lifetime below 30,000 miles, Grear will refund a customer $1 per
100 miles short...

Grear Tire Company has produced a new tire with an estimated
mean lifetime mileage of 36,500 miles. Management also believes
that the standard deviation is 5000 miles and that tire mileage is
normally distributed. To promote the new tire, Grear has offered to
refund a portion of the purchase price if the tire fails to reach
30,000 miles before the tire needs to be replaced. Specifically,
for tires with a lifetime below 30,000 miles, Grear will refund a
customer $1...

The Flamerock Tire company manufactures a particular tire model
that has a mean lifetime of 65,000 miles with a standard deviation
of 4500 miles. The lifetimes are normally distributed. What is the
probability that one of these tires selected at random will last
70,000 miles or more?

(All answers were generated using 1,000 trials and native Excel
functionality.)
Grear Tire Company has produced a new tire with an estimated
mean lifetime mileage of 36,500 miles. Management also believes
that the standard deviation is 5,000 miles and that tire mileage is
normally distributed. To promote the new tire, Grear has offered to
refund some money if the tire fails to reach 30,000 miles before
the tire needs to be replaced. Specifically, for tires with a
lifetime below 30,000...

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INNOVATION
Deep Change: How Operational Innovation Can Transform Your
Company
by
Michael Hammer
From the April 2004 Issue
Save
Share
8.95
In 1991, Progressive Insurance, an automobile insurer based in
Mayfield Village, Ohio, had approximately $1.3 billion in sales. By
2002, that figure had grown to $9.5 billion. What fashionable
strategies did Progressive employ to achieve sevenfold growth in
just over a decade? Was it positioned in a high-growth industry?
Hardly. Auto insurance is a mature, 100-year-old industry...

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