According to Chebychev's theorem, what percentage of a distribution will be within k = 3.7 standard deviations of the mean? (Give your answer correct to one decimal place.)

Answer 1

I don't know about Chebychev's theorem, but this might help.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability of a Z score, which is a standard score in terms of standard deviations.

Answer 2

Here are some facts about Chebychev's Theorem:

Chebyshev's Theorem can be used for a skewed distribution.

This 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%

For your problem, use k = 3.7.
1 - (1/3.7^2)= 1 - (1/13.69) = 1 - 0.073 = 0.927 or 92.7% (approximately)

I hope this will help.