The National Assessment of Educational Progress (NAEP) gave a test of basic arithmetic and the ability to apply it in everyday life to a sample of 840 men 21 to 25 years of age. Scores range from 0 to 500; for example, someone with a score of 325 can determine the price of a meal from a menu. The mean score for these 840 young men was x = 272. We want to estimate the mean score μ in the population of all young men. Consider the NAEP sample as an SRS from a Normal population with standard deviation σ = 60.
If we take many samples, the sample mean x varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population.What is the standard deviation of this sampling distribution?