Are You "Normal"?

SAT Overall Scores

SAT Overall Scores:

  • 1540
  • 1460
  • 1590
  • 1600
  • 1640
  • 1470
  • 1570
  • 1320
  • 1640
  • 1440
  • 1920
  • 2000
  • 1520
  • 1390
  • 1380

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.