In a survey of 859 homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was $64.1 with standard deviation $12.62. Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between $51.48 and $76.72. Round to the nearest whole number.

Question

Mathematics

Wayne Mcmahon

11 January, 14:10

In a survey of 859 homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was $64.1 with standard deviation $12.62. Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between $51.48 and $76.72. Round to the nearest whole number.

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Turner Huynh · Answer 1

68% of the plans cost between $51.48 and $76.72. Of 859, that is 0.68*859 = 584 plans.

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 = 64.1

Standard deviation = 12.62

Estimate the number of plans that cost between $51.48 and $76.72.

64.1 - 12.62 = 51.48

So 51.48 is one standard deviation below the mean.

64.1 + 12.62 = 76.72

So 76.72 is one standard deviation above the mean.

By the Empirical Rule, 68% of the plans cost between $51.48 and $76.72. Of 859, that is 0.68*859 = 584 plans.