Recall from the Central Limit Theorem that the standard error of the mean is equal to the population standard deviation, *s* , divided by the square root of the sample size:

Thus, for a sample of *N* = 5 and population standard deviation of *s* = 100, the standard error of the mean is 100/2.236 or **44.721**.

We know that approximately 95% of scores in a normal distribution are within two standard deviations of the mean (1.96 standard deviations, to be more precise). If the sampling distribution of means is normal, then we expect about **95% of means** from samples with *N* = 5 to be within about 88 points of the actual population mean (1.96 * 44.721 = 87.653), from about **412** to **588** (see figure below).

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