Answer:
0.185185185185185185.........
Step-by-step explanation:
i used a calculator, to the nearst tenth is 0.18 to the nearest 100th is 0.185 also the 185 is repeating so u put a line over the numbers 185
Answer:
\mu = 14.5\\
\sigma = 5.071\\
k = 1.084
Step-by-step explanation:
given that a statistician uses Chebyshev's Theorem to estimate that at least 15 % of a population lies between the values 9 and 20.
i.e. his findings with respect to probability are
![P(9](https://tex.z-dn.net/?f=P%289%3Cx%3C20%29%20%5Cgeq%200.15%5C%5CP%28%7Cx-14.5%7C%3C5.5%29%20%5Cgeq%200.15)
Recall Chebyshev's inequality that
![P(|X-\mu |\geq k\sigma )\leq {\frac {1}{k^{2}}}\\P(|X-\mu |\leq k\sigma )\geq 1-{\frac {1}{k^{2}}}\\](https://tex.z-dn.net/?f=P%28%7CX-%5Cmu%20%7C%5Cgeq%20k%5Csigma%20%29%5Cleq%20%7B%5Cfrac%20%7B1%7D%7Bk%5E%7B2%7D%7D%7D%5C%5CP%28%7CX-%5Cmu%20%7C%5Cleq%20k%5Csigma%20%29%5Cgeq%201-%7B%5Cfrac%20%7B1%7D%7Bk%5E%7B2%7D%7D%7D%5C%5C)
Comparing with the Ii equation which is appropriate here we find that
![\mu =14.5](https://tex.z-dn.net/?f=%5Cmu%20%3D14.5)
Next what we find is
![k\sigma = 5.5\\1-\frac{1}{k^2} =0.15\\\frac{1}{k^2}=0.85\\k=1.084\\1.084 (\sigma) = 5.5\\\sigma = 5.071](https://tex.z-dn.net/?f=k%5Csigma%20%3D%205.5%5C%5C1-%5Cfrac%7B1%7D%7Bk%5E2%7D%20%3D0.15%5C%5C%5Cfrac%7B1%7D%7Bk%5E2%7D%3D0.85%5C%5Ck%3D1.084%5C%5C1.084%20%28%5Csigma%29%20%3D%205.5%5C%5C%5Csigma%20%3D%205.071)
Thus from the given information we find that
![\mu = 14.5\\\sigma = 5.071\\k = 1.084](https://tex.z-dn.net/?f=%5Cmu%20%3D%2014.5%5C%5C%5Csigma%20%3D%205.071%5C%5Ck%20%3D%201.084)
business and education
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