Chapter 3: Q. 3.145 (page 124)

How many standard deviations to either side of the mean must we go to ensure that for any data set, at least $99 %$ of the observations lie within?

Short Answer

Expert verified

At least $99 %$ of the data lies within $k = 10$ standard deviations of the mean.

Step by step solution

Given Information

We have been given that at least $99 %$ of the observation lie within.

Simplification

We know Chebyshev's Rule says that at least $100 (1 - \frac{1}{k^{2}}) %$ of the data values is within k standard deviations from the mean (k>1).

We are interested in finding the number of standard deviations k such that $100 (1 - \frac{1}{k^{2}}) %$ becomes $99 %$ .

So, $100 (1 - \frac{1}{k^{2}}) = 99$

On simplifying, we get

$k^{2} = 100$

$k = 10$

Thus Chebyshev's rule then tells us that at least $99 %$ of the data lies within $k = 10$ standard deviations of the mean.

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How many standard deviations to either side of the mean must we go to ensure that for any data set, at least $99 %$ of the observations lie within?

Short Answer

Step by step solution

Given Information

Simplification

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How many standard deviations to either side of the mean must we go to ensure that for any data set, at least 99%of the observations lie within?

Short Answer

Step by step solution

Given Information

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

How many standard deviations to either side of the mean must we go to ensure that for any data set, at least $99 %$ of the observations lie within?