Elementary Statistics
posted by mary on .
Heights of women have a bellshaped 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?

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.