1. Chapter 5  NORMAL DISTRIBUTION AND Z-SCORE
Understanding Statistics for International Social Work and Other Behavioral Sciences
Serge Lee, Maria C Silveira Nunes Dinis, Lois Lowe, and Kelly Anders (2015). Oxford University Press

2. NORMAL CURVE
The sum of the deviations of all observation scores from the mean is balanced at the center point on the number line, which is equal to or very near zero

3. SKEWED DISTRIBUTION Positively Skewed Distributions
Negatively Skewed Distributions
Lee. Dinis, Lowe, Anders (2015). Understanding statistics for international social work and other behavioral sciences. Oxford University Press

4. STANDARD DEVIATION ON PROPORTION OF THE NORMAL CURVE
The normal curve is divided into six equal units. The six units collectively reflect the variation that exists within virtually all values of a normally distributed interval or ratio level scale variable.
Confidence interval
Lee. Dinis, Lowe, Anders (2015). Understanding statistics for international social work and other behavioral sciences. Oxford University Press

5. DISTANCE BETWEEN THE SAMPLE MEAN AND STANDARD DEVIATION
The proportion between the mean and their corresponding standard deviations are divided as below:
Distance from the mean and standard deviation
1SD
2SD
3SD
Total areas under the normal curve
Left side only of the curve between mean and SD (-SD)
34.13
13.59
2.15
49.87
Right side only of the curve between mean and SD (+SD)
Both sides under areas of the normal curve
68.26
27.18
4.30
99.74
Confidence interval
Lee. Dinis, Lowe, Anders (2015). Understanding statistics for international social work and other behavioral sciences. Oxford University Press

6. CALCULATE THE Z-SCORE AND CONVERT TO A PERCENTILE
Formula:
Z = X− X SD
Statistics rules for the conversion of the Z-score into percentile ranks:
Always round the calculated Z-score to two decimal places. For example, Z = -2.29
If the calculated Z-score is positive (+), add 50% or .50 (if use decimals) to the percentile obtained from the standard normal curve table
If the calculated Z-score is negative (-), subtract the percentile obtained from the critical values of the standard normal curve table from 50% or .50 (if use decimals)