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i have assignment to solve the following problem,

The height of a person is a random variable with variance ≤5 inches2. According to Mr. Chebyshev, how many people do we need to sample to ensure that the sample mean is at most 1 inch away from the distribution mean with probability ≥95%?

i tried solve the problem by first apply weak law of large numbers as follows

P(|x-u|>= a) <= variance/a.n where X is sample mean and n is the sample size.

then, by applying WLLN

P(|X-u| <= 1) <= 1 - 0.95, means variance/1.n = 0.05. and n = 500

however, obtained n=500 is inches number but question requested number of persons. how can i find number of persons given that i correctly calculated number of inches 500.

Ethan Bolker
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Nour
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  • We use a type of $\LaTeX$ called MathJax here. Please search for a tutorial on it :) – Shaun Nov 26 '18 at 15:13
  • No idea where you get “$n=500$ is the number of inches” from. It has nothing to do with inches... it is the sample size. On a more minor note you seem to have forgotten to plug in the variance as $5$: it should be $n=100.$ – spaceisdarkgreen Nov 26 '18 at 15:23
  • your answer is correct Shaun it is n=100 thank you very much, actually i got n=500 when i plug variance as 25, i did so as i got confused due to number "2" after word "inches" in the question, i though it is power of 2. thanks a lot again. – Nour Nov 26 '18 at 15:49

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