A statistician uses Chebyshev's Theorem to estimate that at least 65 % of a population lies between the values 5 and 13. Use this information to find the values of the population mean, u , and the population standard deviation o. a) u = b) o =

A statistician uses Chebyshev's Theorem to estimate that at least 65 % of a population lies between the values 5 and 13. Use this information to find the values of the population mean, u , and the population standard deviation o. a) u = b) o =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

A statistician uses Chebyshev's Theorem to estimate that at least 65% of a population lies between the values 5 and 13. Use this information to find the values of the population mean, $ \mu $, and the population standard deviation $ \sigma $.

a) $ \mu = $ [Input Field]

b) $ \sigma = $ [Input Field]

Expert Solution

Step 1

It is said that atleast 65% of population is
between 5 and 13.

The Chebyshev's inequality states that for a population or sample, the proportion of observations is no less than 1-(1/k^2), given that z scores's absolute value is less than or equal to k.
Therefore, 1-0.65=1/k^2
1/k^2=0.35
k^2=1/0.35
k=sqrt (1/0.35)
k=1.69

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