# If a random sample of size 11 is drawn from a population distribution with standard deviation σ = 10 then what will be the variance of the sampling distribution of the sample mean?

Jan 6, 2018

Variance of the sampling distribution $= \frac{100}{11}$

#### Explanation:

Given-
Sample size $= 11$
Standard Deviation of the population distribution $\sigma = 10$

From the above information, we can get the standard deviation of the sampling distribution or standard error.

$S E = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{11}}$

Variance of the sampling distribution $= {\left(\frac{10}{\sqrt{n}}\right)}^{2} = \frac{100}{11}$
Variance of the sampling distribution $= \frac{100}{11}$