# Normal Distribution Flashcards

Characteristics of the normal distribution

PHOTO 1

Bell-shaped

Symmetrical

Mean, median and mode are equal

Central location is determined by the mean

Spread is determined by the standard deviation (IT IS THE POPULATION STANDARD DEVIATION)

The random variable x has an infinite theoretical range

Many different normal distributions

PHOTO 2 SLIDE 4

Identical mean on yellow and blue

Larger mean on pink

yellow smallest sd

Blue medium sd

Pink largest sd

What is the height of the curve a measure of

Probability

What must the area under the curve be

1

Shape of the normal distribution

Photo 3

Normal distribution always refers to

Population because Greek letters

Translation to the standardised normal distribution

Any normal distribution (with any mean and standard deviation combination) can be transformed into the standardised normal distribution (Z).

Translate any X to the Standardised Normal (the Z distribution) by subtracting the population mean from any particular X value and dividing by the population standard deviation

Normal distribution pdfs

PHOTOS 4-5

The standardised normal distribution

PHOTO 7 SLIDE 9

Also known as the Z distribution

Mean is 0

Standard deviation is 1

Values above the mean have positive Z-values. Values below the mean have negative Z-values.

Standardised normal distribution example

PHOTO 6 Slide 10

General procedure for finding probabilities

To find P(a < X < b) when X is distributed normally:

Draw the normal curve for the problem in terms of X.

Translate X-values to Z-values and put Z values on your diagram.

Use the Standardised Normal Table.

Photo 8

Transformation of scales

Finding the x value for a known probability

Photos 9-12

Methods of evaluating normality

Compare data set characteristics with properties of normal distribution.

Constructing charts and observing their appearance.

Calculate descriptive numerical measures.

Evaluate how data are distributed.

Construct normal probability plot.

Constructing charts and observing their appearance.

- For small- or moderate-sized data sets, do stem-and-leaf display and box-and-whisker plots look symmetric?

For large data sets, does the histogram or polygon appear bell-shaped?