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* = 25 and population standard deviation of* s* = 100, the standard error of the mean is 100/5 or **20**.

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* = 25 to be within about 39 points of the actual population mean (1.96 * 20 = 39.2), from about **461** to **539** (see figure below).