If all the possible random samples with n = 36 scores are selected from a normal population with µ = 50 and σ = 18, and the mean is calculated for each sample, then the Expected Value of M is _ and the Standard Error of M is _?

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, also called standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

µ = 50 and σ = 18

For the sample

Mean 50 and standard error [tex]s = \frac{18}{\sqrt{36}} = 3[/tex].

The answer is:

Expected Value of M is 50 and the Standard Error of M is 3

If all the possible random samples with n = 36 scores are selected from a normal population with µ = 50 and σ = 18, and the mean is calculated for each sample, then the Expected Value of M is _____ and the Standard Error of M is _____?

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If all the possible random samples with n = 36 scores are selected from a normal population with µ = 50 and σ = 18, and the mean is calculated for each sample, then the Expected Value of M is _ and the Standard Error of M is _?