.(16.01) The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth-grade students. Scores on the test range from 0 to 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 stem-and-leaf plot.

In 2013, 170,100 8th-graders were in the NAEP sample for the mathematics test. The mean mathematics score wasx

x

= 285. We want to estimate the mean score

in the population of all 8th-graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation

= 125.

Step 1:

If we take many samples, the sample meanxvaries from sample to sample according to a Normal distribution with mean equal to the unknown mean scorein the population.

What is the standard deviation of this sampling distribution?

Give your answer to 4 decimal places.

Fill in the blank:

Step 2:

According to the 95 part of the 68-95-99.7 rule, 95% of all values ofxfall within ____ on either side of the unknown mean.

What is the missing number?

Give your answer to 4 decimal places.

Fill in the blank:

Fill in the blank

The 95% confidence interval for the population mean scorebased on this one sample is between ____ and ____. (Give your answers to one decimal place.)

Answer 1: ______

Answer 2: _______