Question

The highway miles per gallon rating of the 1999 Volkswagen Passat was 31 mpg (Consumer Reports, 1999). The fuel efficiency that a driver obtains on an individual tank of gasoline naturally varies from tankful to tankful.

Suppose the mpg calculations per tank of gas vary normally with a mean μ = 31 mpg and standard deviation σ = 3 mpg.

According to the Central Limit Theorem, what would be the value of the mean of the sampling distribution if we repeatedly take random samples of size 60 from this population?

Answer 1

Solution :

Given that,

mean = = 31

standard deviation = = 3

n = 60

The sampling distribution of mean is ,

= 31

The sampling distribution of standard deviation is ,  

= / n = 3 / 60 = 0.3873