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6 September, 22:19

Internet providers: In a survey of 935 homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was $74.34 with standard deviation $12.18. Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between $62.16 and $86.52. Round to the nearest whole number.

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  1. 6 September, 22:39
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    68% of plans cost between $62.16 and $86.52.

    Step-by-step explanation:

    The Empirical Rule states that, for a normally distributed random variable:

    68% of the measures are within 1 standard deviation of the mean.

    95% of the measures are within 2 standard deviation of the mean.

    99.7% of the measures are within 3 standard deviations of the mean.

    In this problem, we have that:

    Mean: 74.34

    Standard deviation: 12.18

    Bell-shaped is the same as normally distributed.

    Estimate the number of plans that cost between $62.16 and $86.52.

    62.16 is one standard deviation below the mean.

    86.52 is one standard deviation above the mean.

    By the Empirical rule, 68% of the measures are within 1 standard deviation of the mean.

    So

    68% of plans cost between $62.16 and $86.52.
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