The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighthgrade students. Scores on the test range from 00 to 500.500. Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stemandleafplot.

In 2019, 147,400147,400 eighthgraders were in the NAEP sample for the mathematics test. The mean mathematics score was =282.x=282. We want to estimate the mean score in the population of all eighthgraders. Consider the NAEP sample as an SRS from a Normal population with standard deviation=40

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 in the population. What is the standard deviation of this sampling distribution?

Give your answer to four decimalplaces.

standarddeviation: