# 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; $$E(X)=\mu=n \cdot p$$ $$Var(X)=\sigma^2=n\cdot p \cdot (1-p)$$
• 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
• 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