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The average miles per gallon of a particular automobile model are approximately normally distributed with a given mean u = 43.8 miles per gallon and standard deviation o = 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

Respuesta :

altavistard

Note that 38.7 mpg is one standard deviation below the mean, and that 48.8 mpg is one std dev above the mean. Thus, we're interested in finding the area under the standard normal curve within one std dev of the mean.

According to the Empirical Rule, that percentage is 68%.

Thus, 68% of cars in this pool get between 38.7 and 48.8 mpg.

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

What does the Empirical Rule state?

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, we have that the mean is of 43.8 mpg, and the standard deviation is of 5.1 mpg, then:

  • 38.7 = 43.8 - 5.1.
  • 48.9 = 43.8 + 5.1.

Within 1 standard deviation of the mean, hence, 68% of the automobiles have an average mpg between 38.7 and 48.9.

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

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