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In: Statistics and Probability

For the following sample sizes of 100, 50, and 20 I got the following data values....

For the following sample sizes of 100, 50, and 20 I got the following data values. I was asked the proportion of x students on a assingment with a vairiety of test scores. It asked for the proportion of students getting higher than a 69 and 90.

The population mean : 83.516

Sample of 100 mean = 81.91
Sample of 50 = 81.74
Sample of 20 = 84.05

for above 69 i got the following proportions

Population proportion = .886
Sample of 100 = .86
Sample of 50 = .86
Sample of 20 = .90

For above 90 I got

Population proportion = .162
Sample of 100 = .15
Sample of 50 = .02
Sample of 25 = .2

Do the following means and proportion values hold true to the central limit theorem? Why? Or Why not? What should the values do to uphold the central limit theorem?

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