Answer:
a) The z-score for the mileage of the car is -3.16
b) It appears that the car is getting unusually low gas mileage.
Step-by-step explanation:
The z-score formula is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which: X is the mileage per gallon we are going to find the z-score of, [tex]\mu[/tex] is the mean value of this mileage and [tex]\sigma[/tex] is the standard deviation of this value.
a. Find the z-score for the gas mileage of your car, assuming the advertised claim is correct.
The gas mileage for you car is 16.4 mpg, so [tex]X = 16.4[/tex]
The advertised gas mileage is 20 mpg, so [tex]\mu = 20[/tex]
The standard deviation is 1.14 mpg, so [tex]\sigma = 1.14[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma} = \frac{16.4 - 20}{1.14} = -3.16[/tex]
b. Does it appear that your car is getting unusually low gas mileage?
The general rule is that a z-score lower than -1.96 is unusually low. So yes, it appears that the car is getting unusually low gas mileage.
