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According to the U.S. Census​ Bureau, the mean of the commute time to work for a resident of CA is 21.5 minutes. Assume that the standard deviation of the commute time is 4.8 minutes to complete parts​ (a) through​ (c).

Part 1
​(a) What minimum percentage of commuters in has a commute time within standard deviations of the​ mean?

enter your response here​% ​
(Round to one decimal place as​ needed.)

Sagot :

Using Chebyshev's Theorem, the minimum percentage of commuters in has a commute time within 2 standard deviations of the​ mean is of 75%.

What does Chebyshev’s Theorem state?

When we have no information about the population distribution, Chebyshev's Theorem is used. It states that:

  • At least 75% of the measures are within 2 standard deviations of the mean.
  • At least 89% of the measures are within 3 standard deviations of the mean.
  • An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

Hence, the minimum percentage of commuters in has a commute time within 2 standard deviations of the​ mean is of 75%.

More can be learned about Chebyshev's Theorem at https://brainly.com/question/23612895

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