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?

Brugolino7t

Brugolino7t

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2022-08-20

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?

Answer & Explanation

Andre Ferguson

Andre Ferguson

Beginner2022-08-21Added 12 answers

Explanation:
we are not told what the background distribution is. But since the sample size is > 30 we can use the Central Limit Theorem.
if X ¯ is the sample mean the sampling distribution is approximately Normal given by
X ¯ N ( μ , σ 2 n )
in this case we have
X ¯ N ( 50 , 20 2 100 )
the mean will be μ m = 50
standard error σ m = 20 2 100 = 20 10 = 2

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