Statistics Homework Question

Question

Suppose you buy a new car whose advertised mileage is 22 miles per gallon (mpg). After driving your car for several months, you find that its mileage is 17.4 mpg. You telephone the manufacturer and learn that the standard deviation of gas mileages for all cars of the model you bought is 1.27 mpg. a. Find the z-score for the gas mileage of your car, assuming the advertised claim is correct. b. Does it appear that your car is getting unusually low gas mileage?

Answer 1

z = (x-μ)/σ where:

• z = the z-score for the data point x
• x = the data point = 17.4 mpg
• μ = the mean of the data set = 22 mpg
• σ = the standard deviation of the data set = 1.27 mpg

 

z = (x-μ)/σ

z = (17.4 - 22)/1.27 = -3.62

 

Yes, you are 3.62 standard deviations below the mean.  Standard z score tables (http://www.z-table.com/) only go to -3.49.  So the car gets fewer mpg than 99.998% of other cars of the same type.

Answer 2

find the difference between the mean and the observed value 17.4

then divide this difference by the standard deviation.

That is the z score

about 68% of all scores should fall between -1 and +1 z-scores.

about 97% should fall between -2 and +2 z scores.

Can you decide NOW?