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The average miles per gallon of a particular automobile model are approximately normally distributed with a given mean Mu = 43.8 miles per gallon and standard deviation Sigma = 5.1 miles per gallon. What percentage of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon? 68% 75% 95% 100%

Answer :

Answer: A.68%

Step-by-step explanation: I just did it!

Using the Empirical Rule, it is found that 68% of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon.

What is the Empirical Rule?

It states that, for a normally distributed random variable:

  • Approximately 68% of the measures are within 1 standard deviation of the mean.
  • Approximately 95% of the measures are within 2 standard deviations of  the mean.
  • Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, the mean is of 43.8 mpg and the standard deviation is of 5.1 mpg, hence:

43.8 - 5.1 = 38.7

43.8 + 5.1 = 48.9

68% of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon.

More can be learned about the Empirical Rule https://brainly.com/question/24537145

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