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.

Question

Mathematics

Cailyn Peterson

8 November, 13:51

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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Answers (1)

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Alisa Newton · Answer 1

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.