# American automobiles produced in 2012 and classifiedas “large” had a mean fuel economy of 19.6 miles pergallon with a standard deviation of 3.36 miles per gallon.

American automobiles produced in 2012 and classified as “large”; had a mean fuel economy of 19.6 miles per gallon with a standard deviation of 3.36 miles per gallon. A particular model on this list was rated at 23 miles per gallon, giving it a z-score of about 1.01. Which statement is true based on this information?

A) Because the standard deviation is small compared to the mean, a Normal model is appropriate and we can say that about $$84.4\%$$ of of large automobiles have a fuel economy of 23 miles per gallon or less.

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Step 1

Normal distribution is used in various real life applications. It is a two-parameter distribution which denotes its mean and variance correspondingly. One of the properties is that the linear combination of number of random variables also has normal distribution which helps a lot in modeling.

Step 2 The statement

A) is true based on this information which is "Because the standard deviation is small compared to the mean, a Normal model is appropriate and we can say that about $84.4\mathrm{%}$ of large automobiles have a fuel economy of 23 miles per gallon or less.