Question

5. Suppose that a car manufacturer claims that its fuel efficiency (as measured in miles per
gallon) per tankful of gasoline follows a normal distribution with mean 35 mpg and
standard deviation 2.0 mpg.
a) What percentage of tankfuls would obtain between 30 and 40 mpg? (A table of
standard normal probabilities appears at the end of this exam.)
b) Would the percentage of tankfuls that obtain between 30 and 40 mpg be larger,
smaller, or the same if the mean were larger than 35 (and the SD remained 2.0)? Explain your
answer.
c) Would the percentage of tankfuls that obtain between 30 and 40 mpg be larger, smaller,
or the same if the SD were larger than 2.0 (and the mean remained 35)? Explain your answer.

Answer 1

The distribution here is given as:

a) The probability here is computed as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 98.76% is the required percentage here.

b) For a normal distribution, the majority of the frequencies lies bear the mean. Therefore if we move mean anywhere right or left of 35, the percentage would decrease. (between 30 and 40)

c) For a greater standard deviation, there would be lesser number of observations near the mean. Therefore for a larger SD than 2, the percentage would decrease.