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I can't figure out how to calculate P(4 < X < 12) using Chebyshev's. It's given that mean = 7.9 and variance = 7.9

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  • $\begingroup$ are you sure the mean is 7.9 and not 8? $\endgroup$ – tommik Oct 17 at 21:30
  • $\begingroup$ the theoretical mean is 8 but the empirical mean is 7.9 so I guess you're right about that $\endgroup$ – yeetbro Oct 17 at 21:31
  • $\begingroup$ Sounds like there are some relevant details in the problem that you haven't told us about... $\endgroup$ – Ian Oct 17 at 21:39
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If the theoretical mean is 8 you have just to apply Chebyshev inequality:

$$\mathbb{P}\{|X-\mu|<\epsilon\}\geq 1-\frac{\sigma^2}{\epsilon^2}$$

Sustituting, you get

$$\mathbb{P}\{|X-8|<4\}\geq 1-\frac{7.9}{4^2}=0.50625$$

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