Suppose the brain volume for adult women is about 1,100 cc, with a standard deviation of 75 cc. Then consider a sample of 144 random women taken from this population, with an unspecified sample mean. Determine the approximate 10th percentile of the distribution of the distribution of sample means of the 144 women?
The solution to this problem hinges on the determination that the standard deviation of the sample mean is $75/12 = 6.25$. But why is this true? How could we possibly justify this? Where does the number, 12, come from?