Given: Mean () = 22,000 miles Standard deviation () = 3,100 miles The manufacturer wants to ensure that no more than 3% of tires will qualify for a refund. We'll find the z-score corresponding to the 3rd percentile (since we want to ensure that 97% of tires do not qualify for a refund) and then use it to find the corresponding mileage value. First, let's find the z-score corresponding to the 3rd percentile: = invNorm ( 0.03 ) z=invNorm(0.03) Using a standard normal distribution table or calculator, we find 1.8808 z1.8808. Now, we use the z-score formula to find the minimum number of miles (X): = z= X 1.8808 = 22 , 000 3 , 100 1.8808= 3,100 X22,000 1.8808 3 , 100 = 22 , 000 1.88083,100=X22,000 5822.68 = 22 , 000 5822.68=X22,000 = 5822.68 + 22 , 000 X=5822.68+22,000 16 , 177.32 X16,177.32 Rounded to the nearest whole number, the minimum number of miles the manufacturer should guarantee that the tires will last is 16,177 miles. Therefore, the correct option is 16,170