Elementary Statistics

Heights of women have a bell-shaped distribution with a mean of 161 cm and a standard deviation of 7 cm. Using Chebyshev’s theorem, what do we know about the percentage of women with heights that are within 2 standard deviations of the mean? What are the minimum and maximum heights that are within 2 standard deviations of the mean?

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  1. Chebyshev's Theorem says:

    1. Within two standard deviations of the mean, you will find at least 75% of the data.
    2. Within three standard deviations of the mean, you will find at least 89% of the data.

    Here's how the formula shows this:
    Formula is 1 - (1/k^2) ---> ^2 means squared.

    If k = 2 (representing two standard deviations), we have this:
    1 - (1/2^2) = 1 - (1/4) = 3/4 or .75 or 75%

    If k = 3 (representing three standard deviations), we have this:
    1 - (1/3^2) = 1 - (1/9) = 8/9 or approximately .89 or 89%

    I'll let you take it from here.

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