Question

In: Advanced Math

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.


  3. 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

Solutions

Expert Solution

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:


Related Solutions

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...
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...
Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500...
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...
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.
(All answers were generated using 1,000 trials and native Excel functionality.) Grear Tire Company has produced...
(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...
SunLight Company is planning to manufacture a new lightbulb with an estimated mean lifetime run of...
SunLight Company is planning to manufacture a new lightbulb with an estimated mean lifetime run of 36,500 hours. Management also believes that the standard deviation is 5,000 hours, and that the lifetime hours are normally distributed. Essay Questions A. Use Excel to simulate the hours obtained from a sample of 500 lightbulbs, and use the COUNTIF function to determine the number of bulbs that last longer than 40,000 hours. What is your estimate of the percentage of bulbs that will...
The lifetime of a particular brand of tire is modeled with a normal distribution with mean...
The lifetime of a particular brand of tire is modeled with a normal distribution with mean μ = 75,000 miles and standard deviation σ = 5,000 miles. a) What is the probability that a randomly selected tire lasts less than 67,000 miles? b) If a random sample of 35 tires is taken, what is the probability that the sample mean is greater than 70,000 miles?
1) The mean lifetime of a tire is 36 months with a variance of 49. If...
1) The mean lifetime of a tire is 36 months with a variance of 49. If 126 tires are sampled, what is the probability that the mean of the sample would differ from the population mean by greater than 0.44 months? Round your answer to four decimal places. 2) Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.5 years with a standard deviation of 1.1 years. a) If a...
A dishwasher has a mean lifetime of 12 years with an estimated standard deviation of 1.25...
A dishwasher has a mean lifetime of 12 years with an estimated standard deviation of 1.25 years. Assume the lifetime of a 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 a lifetime of 8.25 years or more. c) Find the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT