Module 3: 3-1: Normal Distribution pt. 2

Nearly Normal Condition

shape of data’s distribution is unimodal and symmetric, can be checked by making a histogram or normal plot

Normal Probability plot

graphic display that aids with deciding if a model is appropriate

• normal: straight diagonal line

• not normal: deviates from a straight line

Empirical Rule

applies to normal distributions and distributions easily described by a normal curve: 68-95-99.7 rule

68-95-99.7 rule

• 68%: fall within 1o of mean u

• 95% fall within 2o of mean u

• 99.7% fall within 3o of mean u

Normal Distribution: Probability values

Use Table z

cumulative area/proportion

z*: area under the curve from infinity to z

Table z: negative values

lower half of curve

Table z: positive values

upper half of curve

Normal Distribution Theorem

if y is normal distributed with mean and standard deviation, the standardized variable is normal distributed with:

• u: 0

• o: 1 or z~N(0.1)