The members of Maggie's choir have a mean height of 58 inches, with a standard deviation of 4 inches. The choir includes both children and adults, and the distribution of their heights is not symmetric, Between what two heights does Chebyshev's Theorem guarantee that we will find at least approximately 89 % of the choir members?

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Mathematics

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2 August, 07:32

The members of Maggie's choir have a mean height of 58 inches, with a standard deviation of 4 inches. The choir includes both children and adults, and the distribution of their heights is not symmetric, Between what two heights does Chebyshev's Theorem guarantee that we will find at least approximately 89 % of the choir members?

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Abigayle Cherry · Answer 1

Chebyshev's theorem guarantees that we will find at least approximately 89 % of the choir members between 46 and 70 inches.

Step-by-step explanation:

Chebyshev's Theorem states that, in a sample:

75% of the measures are within 2 standard deviations of the mean

89% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 58

Standard deviation = 4

Between what two heights does Chebyshev's Theorem guarantee that we will find at least approximately 89 % of the choir members?

Within 3 standard deviations the mean, so from 3 standard deviations below the mean to 3 standard deviations above the mean.

3 standard deviations below the mean

58 - 3*4 = 46

3 standard deviations above the mean

58 + 3*4 = 70

Chebyshev's theorem guarantees that we will find at least approximately 89 % of the choir members between 46 and 70 inches.