Bobs Company has produced a new tire with an estimated mean lifetime mileage of
ID: 1720517 • Letter: B
Question
Bobs 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. 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 nd the number of tires that obtain mileage less than 32,000 miles. Then, nd the number with less than 30,000 miles and the number with less than 28,000 miles
Please use excel and show all formulas
Explanation / Answer
a) COUNTIF function takes the two arguements range and the criteria
A1 = Distance travelled by the car
A2 = Condition to count
A3 = number of samples
COUNTIF(A1,A2,A3)
Zscore = (X-mean)/sigma = (40000-36500)/5000 = 0.7
P(Z>0.7) = 1 - P(Z<0.7)
=> 1 - 0.75804
=> 0.24196
Hence the estimated percentage will be 24.196%
b) Z = (32000-36500)/5000 = -0.9
P(Z<-0.9) = 0.184
Z = (30000-36500)/5000 = -1.3
P(Z<-1.3) = 0.09680
Z = (28000-36500)/5000 = -1.6
P(Z<-1.6) = 0.04457