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Can anyone help me with homework? I can`t catch a basic idea of the next exercise: $$ X\thicksim Bin(20,0.2)\\P(|X-\mu|\le\sigma)=? $$ Can anyone at least explain how it opens,please?

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Hint: We have for a Binomial distribution; $$E(X)=\mu=n \cdot p$$ $$Var(X)=\sigma^2=n\cdot p \cdot (1-p)$$

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  • $\begingroup$ Thanx, but I know already that. I just don`t know what to do with this information $\endgroup$ – Hillbilly Joe Feb 2 at 17:26
  • $\begingroup$ Well we then have to calculate $P(|X - 4| \le \sqrt{3.2}) = P((4-\sqrt{3.2}) \le X \le (4+\sqrt{3.2}))$ $\endgroup$ – Peter Foreman Feb 2 at 17:31
  • $\begingroup$ That is what I just tried to do using PDF function, but I get quite strange results of that. $\endgroup$ – Hillbilly Joe Feb 2 at 17:37
  • $\begingroup$ As the binomial distribution is discrete we should only be finding $P(3 \le X \le 5)$ but this is equivalent to what I gave above. i.e $0.59812...$ $\endgroup$ – Peter Foreman Feb 2 at 17:39
  • $\begingroup$ Thanx, your explanation was helpful $\endgroup$ – Hillbilly Joe Feb 2 at 17:43

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