# Are You "Normal"?

• 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.