A population distribution has mean 50 and standard deviation 20. For a random sample of size 100, what is the mean and standard error of the sampling distribution of the sample mean?

Question

14962 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-30T08:11:19

$mu_m=50$

$sigma_m=sqrt(20^2/100)=20/10=2$

we are not told what the background distribution is. But since the sample size is $>30$ we can use the Central Limit Theorem.

if $" "barX$ is the sample mean the sampling distribution is approximately Normal given by

$barX~N(mu, sigma^2/n)$

in this case we have

$barX~N(50, 20^2/100)$

the mean will be $mu_m=50$

standard error $sigma_m=sqrt(20^2/100)=20/10=2$