Question

At a certain dealership with a large number of cars, the mileages on the cars are approximately normally distributed with mean 50,000 miles and standard deviation 12,500 miles. Mr. Randall just bought a car from this dealership with 60,000 miles on it.

Which statements are true about his car compared to the cars at the dealership? Select TWO that apply.


The z-score associated with the mileage on his car is 0.8.


The z-score associated with the mileage on his car is 1.25.


His car has less mileage than approximately 11% of the cars at the dealership.


His car has less mileage than approximately 21% of the cars at the dealership.


His car has less mileage than approximately 79% of the cars at the dealership.


His car has less mileage than approximately 89% of the cars at the dealership.

Answer 1

True statements:
- The z-score associated with the mileage on his car is 0.8.
- His car has less mileage than approximately 21% of the cars at the dealership.

Work: z = (60000 − 50000)/12500 = 0.8. Φ(0.8) ≈ 0.788 → about 78.8% of cars have mileage ≤ 60,000, so about 21.2% have mileage > 60,000 (i.e., his car has less mileage than ~21% of cars).