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]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e0d396c-e5f5-46c2-813a-9ed0820c37ca%2Fb3b8c7b3-9537-46e4-b5ef-3d21b70f1fed%2Fmwy5o1f_processed.png&w=3840&q=75)
Transcribed Image Text: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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