# Problem 16-03 Grear Tire Company has produced a new tire with an estimated mean lifetime mileage...

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. 1. For each tire sold, what is the expected cost of the promotion? If required, round your answer to two decimal places. 2. What is the probability that Grear will refund more than$50 for a tire? If required, round your answer to three decimal places.

##### The operation manager at a tire manufacturing company believes that the mean mileage of a tire...
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...
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 standard deviation of 1.25...
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##### A tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the...
A tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obtained by all tires of this new type is normally distributed with a mean of 39,531 miles and a standard deviation of 4,075 miles. The company wishes to offer a guarantee providing a discount on a new set of tires if the original tires purchased do not exceed the mileage stated in the guarantee. What should the guaranteed mileage be if...
##### The manager of a firm announced: “The lightbulbs produced by our firm have a mean lifetime...
The manager of a firm announced: “The lightbulbs produced by our firm have a mean lifetime of 2,500 hours, with a standard deviation of 250 hours; thus, it follows that approximately 95 percent of our lightbulbs last between 2000 and 3,000 hours.” What was the manager assuming? What if the assumption did not hold – what percentage of the lightbulbs could you expect would last between 2,000 and 3,000 hours?
##### Transistors produced by one machine have a lifetime that is exponential distributed with mean 50 hours....
Transistors produced by one machine have a lifetime that is exponential distributed with mean 50 hours. Those produced by another machine have a lifetime that is exponential distributed with mean 100 hours. A package of transistors contains 3 produced by the first machine and 9 produced by the second machine. Let X be the lifetime of a transistor picked at random from this package. Find: (a) the cdf of X (b) P(X > 150) (c) the pdf of X (d)...
##### A major oil company has developed a new gasoline additive that is supposed to increase mileage....
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)d=(gas mileage with additive)−(gas mileage without additive). Use a significance level of α=0.05α=0.05 for the...
##### A major oil company has developed a new gasoline additive that is supposed to increase mileage.
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...