The Graduate Record Examination (GRE) is a standardized test that students usually take before entering graduate school. According to the document Interpreting Your GRE Scores, a publication of the Educational Testing Service, the scores on the quantitative portion of the GRE are (approximately) normally distributed with mean 584 points and standard deviation 151 points.
a. Use the technology of your choice to simulate 1000 samples of four GRE scores each.
b. Find the sample mean of each of the 1000 samples obtained in part (a).
c. Obtain the mean, the standard deviation, and a histogram of the 1000 sample means.
d. Theoretically, what are the mean, standard deviation, and distribution of all possible sample means for samples of size 4?
e. Compare your answers from parts (c) and (d).