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?

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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#