In: Advanced Math

**Problem 16-03**

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 of 30,000.

- For each tire sold, what is the expected cost of the promotion?
If required, round your answer to two decimal places.

- What is the probability that Grear will refund more than $50
for a tire? If required, round your answer to three decimal
places.

- What mileage should Grear set the promotion claim if it wants
the expected cost to be $2.00? If required, round your answer to
the hundreds place.

miles

**Solution:**

Formula used for simulation of tire life in Excel range B2:B502 =NORMINV(RAND(),36500,5000)

The simulation model in excel and calculation of the answers is given below alongwith formulas:

Problem 16-03
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...

The operation manager at a tire manufacturing company believes
that the mean mileage of a tire is 23,383 miles, with a variance of
21,436,900. What is the probability that the sample mean would be
less than 22,909 miles in a sample of 286 tires if the manager is
correct? Round your answer to four decimal places.

The operation manager at a tire manufacturing company believes
that the mean mileage of a tire is 47,225 miles, with a standard
deviation of 3178 miles. What is the probability that the sample
mean would be greater than 47,050 miles in a sample of 208 tires if
the manager is correct? Round your answer to four decimal
places.

A dishwasher has a mean lifetime of 12 years with an estimated
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dishwasher is normally distributed. Round the probabilities to four
decimal places. It is possible with rounding for a probability to
be 0.0000.
a) State the random variable. rv X = the lifetime of a randomly
selected dishwasher Correct
b) Find the probability that a randomly selected dishwasher has
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c) Find the...

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What was the manager assuming?
What if the assumption did not hold – what percentage of the
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A major oil company has developed a new gasoline additive that
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Let d=(gas mileage with additive)−(gas mileage without
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A major oil company has developed a new gasoline additive that is supposed to increase mileage. To test this hypothesis, ten cars are randomly selected. The cars are driven both with and without the additive. The results are displayed in the following table. Can it be concluded, from the data, that the gasoline additive does significantly increase mileage? Let d=(gas mileage with additive)−(gas mileage without additive). Use a significance level of α=0.05 for the test. Assume that the gas...

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