# Normal Distribution Flashcards

1
Q

Characteristics of the normal distribution

PHOTO 1

A

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

2
Q

Many different normal distributions

A

PHOTO 2 SLIDE 4

Identical mean on yellow and blue

Larger mean on pink

yellow smallest sd
Blue medium sd
Pink largest sd

3
Q

What is the height of the curve a measure of

A

Probability

4
Q

What must the area under the curve be

A

1

5
Q

Shape of the normal distribution

A

Photo 3

6
Q

Normal distribution always refers to

A

Population because Greek letters

7
Q

Translation to the standardised normal distribution

A

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```
8
Q

Normal distribution pdfs

A

PHOTOS 4-5

9
Q

The standardised normal distribution

PHOTO 7 SLIDE 9

A

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.

10
Q

Standardised normal distribution example

A

PHOTO 6 Slide 10

11
Q

General procedure for finding probabilities

A

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.

12
Q

Photo 8

A

Transformation of scales

13
Q

Finding the x value for a known probability

A

Photos 9-12

14
Q

Methods of evaluating normality

A

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.

15
Q

Constructing charts and observing their appearance.

A
• 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?
16
Q

Calculate descriptive numerical measures.

A

Do the mean and median have similar values? (Remember there may be no unique mode or there may be multiple modes.)
Is the interquartile range approximately 1.33 times the standard deviation?
Is the range approximately 6 times the standard deviation?

17
Q

Evaluate how data are distributed.

A

Do approximately 2/3 of the observations lie within mean 1 standard deviation?
Do approximately 80% of the observations lie within mean 1.28 standard deviations?
Do approximately 95% of the observations lie within mean 2 standard deviations?

18
Q

Normal probability plot

A

Arrange data into ordered array.
Find corresponding standardised normal quantile values.
Plot the pairs of points with observed data values on the vertical axis and the standardised normal quantile values on the horizontal axis.
Evaluate the plot for evidence of linearity.

19
Q

Normal probability plot example

A

Photos 13-14

20
Q

Continuous probability density function

A

Mathematical expression that defines the distribution of the values for a continuous random variable.