Question

Lamar is shopping for a three or four year old used car. One important factor to him is the mileage on the car. Here's what he knows:

• Four-year-old cars have a mean mileage of 56,680 with a standard deviation of 17,820.
• Three-year-old cars have a mean mileage of 33,330 with a standard deviation of 12,700.
• Both distributions are approximately Normally distributed.  

1.One car that Lamar is interested in is four years old and has been driven 40,000 miles. Find the z-score for this car (round to two decimal places).

2. Another car is three years old and has 30,000 miles on it. Find the z-score for this car (round to two decimal places).

3. Use the z-scores to compare the number of miles on these cars, relative to other cars of the same age.

Answer 1

The z score for any score from a normal distribution is computed as:

a) For the four year old used car, the z score here is computed as:

Therefore -0.94 is the required z score here.

b) For the three year old used car, the z score here is computed as:

Therefore - 0.26 is the required z score here.

c) From the above computed z scores, we see here that for the z score in part a), which is lower than the z score in car b, therefore the miles of cars driven in part a) is lower corresponding to the miles driven by car in part b) in their respective groups.