the mean of the commute time to work for a resident of a certain city is 28.8 minutes. assume the standard deviation of the commute time is

Question

the mean of the commute time to work for a resident of a certain city is 28.8 minutes. assume the standard deviation of the commute time is 8.1 minutes. what minimum percentage of the commuters in the city has a commute time within 2 standard deviations of the mean?

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Claire 2 weeks 2021-09-26T18:49:43+00:00 1 Answer 0

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    2021-09-26T18:51:32+00:00

    Answer:

    The minimum percentage of the commuters in the city has a commute time within 2 standard deviations of the mean is 75%.

    Step-by-step explanation:

    We have no information about the shape of the distribution, so we use Chebyshev’s Theorem to solve this question.

    Chebyshev Theorem

    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 100(1 - \frac{1}{k^{2}}).

    Applying the Theorem

    The minimum percentage of the commuters in the city has a commute time within 2 standard deviations of the mean is 75%.

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