Q.Find the sample size for the given standard deviation 10 and the standard error with respect of sample mean is 3.

$n=\left(\dfrac{\sigma}{\text{S.E.}}\right)^2=\left(\dfrac{10}{3}\right)^2=\dfrac{100}{9}\approx11.11\Rightarrow n\approx12$.

The standard error of the sample mean is

$\text{S.E.}=\frac{\sigma}{\sqrt n}.$

Given $\sigma=10$ and $\text{S.E.}=3$:

$3=\frac{10}{\sqrt n}\ \Rightarrow\ \sqrt n=\frac{10}{3}=3.333\ \Rightarrow\ n=\left(\frac{10}{3}\right)^{2}=\frac{100}{9}\approx 11.11.$

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