Are You "Normal"?
SAT Overall Scores
Population
Mean- 1565.33
Standard Deviation- 187.38
Z-Scores & Probability
Probability of less than 1600- z = .1850, probability = .5734
Probability between 1320 and 2000- z = -1.3093 & 2.3197, probability = .8946
Probability of greater than 1440- z = -.6689, probability = .7482
Sample Means, Mean of the Sample Means, & Standard Error of the Means
1540
1460
1590
X = 1530
1600
1640
1470
X = 1570
1570
1320
1640
X = 1510
1440
1920
2000
X = 1786.67
1520
1390
1380
X = 1430
µx = 1565.334
ox by calculator- 133.83
ox by formula- 108.18
Population Mean vs Mean of the Sample Means
The data supports that the mean of the sample means equals the population mean.
Standard Deviation of the Sample Means vs Standard Error
Without using the formula the standard deviation is higher, because the one sample mean is around 200 greater than the rest.