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Chapter 3: Q. 3.146 (page 124)

How many standard deviations to either side of the mean must we go to ensure that for any data set, at least 95%of the observations lie within?

Short Answer

Expert verified

At least 95% of the data lies within k=4.47 standard deviations of the mean.

Step by step solution

01

Given Information

We have been given that at least 95%of the observation lie within.

02

Simplification

We know Chebyshev's Rule says that at least 100(1-1k2)%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(1-1k2)%becomes localid="1650702396373" 95%.

So,100(1-1k2)=95

On simplifying, we get

k2=20

k=25

k=4.47

Thus Chebyshev's rule then tells us that at least 95%of the data lies within k=4.47 standard deviations of the mean.

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