# Math Help - Question using Chebyshev's inequality

1. ## Question using Chebyshev's inequality

Right, fingers crossed this questions come out OK:

My inital thought is where do I start? I don't quite understand the question

2. Since $X_i$'s have mean $\mu$ and variance $\sigma^2$ for each $i$, then $\bar{X}$ has mean $\mu$ and variance $\frac{\sigma^2}{n}$. Consequently, the Chebyshev's inequality can be rewritten for $\bar{X}$ as:

$P(|\bar{X}-\mu|\geq a)\leq \frac{\sigma^2}{na^2}$

$=>P(\bar{X}\geq \mu+a, \bar{X}\leq \mu-a)\leq\frac{\sigma^2}{na^2}$ (breaking the modulus sign)

So $\frac{\sigma^2}{na^2}$ is the required upper limit.