# Binomial distribution with mean and standard deviation

Can anyone help me with homework? I cant 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?

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

• Thanx, but I know already that. I just dont know what to do with this information – Hillbilly Joe Feb 2 at 17:26
• Well we then have to calculate $P(|X - 4| \le \sqrt{3.2}) = P((4-\sqrt{3.2}) \le X \le (4+\sqrt{3.2}))$ – Peter Foreman Feb 2 at 17:31
• That is what I just tried to do using PDF function, but I get quite strange results of that. – Hillbilly Joe Feb 2 at 17:37
• 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 $0.59812...$ – Peter Foreman Feb 2 at 17:39
• Thanx, your explanation was helpful – Hillbilly Joe Feb 2 at 17:43
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