According to internal testing done by the Get-A-Grip tire company, the mean lifetime of tires sold on new cars is 23,000 miles, with a standard deviation of 2500 miles.

Question

a) If the claim by Get-A-Grip is true, what is the mean of the sampling distribution of for samples of size ? (2 pts)

b) If the claim by Get-A-Grip is true, what is the standard deviation of the sampling distribution of for samples of size ? (4 pts)

c) If the distribution of tire life is approximately normal, what is the probability that the mean of a random sample of size n = 4 of tire lifetimes will be less than 20,000 miles? (6 pts)

Answer 1

a) The mean of the sampling distribution of tire lifetimes for samples of size n is 23,000 miles.

b) The standard deviation of the sampling distribution of tire lifetimes for samples of size n is 2500/√n miles.

c) The probability that the mean of a random sample of size n = 4 of tire lifetimes will be less than 20,000 miles is 0.0668.