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.)

Question

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.

Answer 3

Chebychev's theorem states that for any distribution, regardless of its shape, at least (1 - (1/k^2)) * 100% of the data will be within k standard deviations of the mean.

In this case, k = 3.7 standard deviations. So, we can calculate the percentage using the formula:

Percentage = (1 - (1/k^2)) * 100%

Substituting k = 3.7 into the formula:

Percentage = (1 - (1/3.7^2)) * 100%

Calculating the value:

Percentage = (1 - (1/13.69)) * 100%
= (1 - 0.073) * 100%
= 0.927 * 100%
= 92.7%

Therefore, according to Chebychev's theorem, approximately 92.7% of the distribution will be within 3.7 standard deviations of the mean.

Answer 4

To determine the percentage of a distribution within k standard deviations of the mean using Chebyshev's theorem, you can use the formula:

Percentage = 1 - (1/k^2)

In this case, k = 3.7. So we can substitute this value into the formula:

Percentage = 1 - (1/3.7^2)

Now, let's calculate it:

Percentage = 1 - (1/13.69)
= 1 - 0.073

Therefore, the percentage of the distribution within 3.7 standard deviations of the mean, according to Chebyshev's theorem, is approximately 92.7%.