Problem 12-17 (Algorithmic) Grear Tire Company has produced a new tire with an e

Question

Problem 12-17 (Algorithmic) Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 37,000 miles. Management also believes that the standard deviatian is 5500 miles and that tire mileage is normally distributed. Use a worksheet to simulate the miles obtained for a sample of 500 tires. a, Use the Excel COUNTIF function to determine the number of tires that last longer than 40,000 miles, What is your estimate of the percentage of tires that will exceed 40,000 miles? b. Use coUNTIF to find the number of tires that obtain mileage less than 32,000 miles. Then find the number with less than 30,000 miles and the number with less than 28,000 miles. Mileage less than 32,000 less than 30,000 less than 28,000 Approximate Percentage c 1 management would like to advertise a tire mileage guarantee such that approximately no more than 10% o the tires would obtain mileage low enough to qualify or the guarantee what tire mileage considered in part b would you recommend for the guarantee 30000 miles or 28000 miles

Explanation / Answer

Solution:

a) Use the Excel COUNTIF function to determine the number of tires that last longer than 40,000 miles. What is your estimate of the percentage of tires that will exceed 40,000 miles.

For the generated data, using Excel COUNTIF function to determine the number of tires that last longer than 40,000 miles. is =COUNTIF(A2:A501,">=40000") =176

What is your estimate of the percentage of tires that will exceed 40,000 miles.

The estimate of the percentage of tries that will exceed 40,000 miles is 176/500 = 34.80%

b) Use COUNTIF to find the number of tires that obtain mileage less than 32,000 miles.

For the generated data, using Excel COUNTIF function to determine the number of tires that less than 32,000 miles. is =COUNTIF(A2:A501,"<32000") =96

For the generated data, using Excel COUNTIF function to determine the number of tires that less than 30,000 miles. is =COUNTIF(A2:A501,"<30000") =55

For the generated data, using Excel COUNTIF function to determine the number of tires that less than 28,000 miles. is =COUNTIF(A2:A501,"<28000") =30

c) I Would recomend Option A because the rate to qualify for the guarantee is good in this range

Mileage Approximate Percentage 32000 96/500 = 19.20% 30000 55/500 = 11.0% 28000 30/500 = 6.0%

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