Skip to main content
1 of 4
Aksakal
  • 62.3k
  • 6
  • 106
  • 206

If you have upper and lower bounds M and 0, then you can apply Popovivicu's upper bound on variance: $$\sigma^2<\frac 1 4(M-m)^2$$

Once you have the variance, apply usual sample mean distribution logic, i.e. the variance of a sample mean $\bar x$ to be $\sigma^2_{\bar x}\sim\sigma^2/n$. The rest is trivial.

Aksakal
  • 62.3k
  • 6
  • 106
  • 206