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Normal curve

Normal curve

- The curve is symmetric about the mean.
- Each half represents 50 of the total area.
- The total area is 1.0000
- Areas can be thought of as probabilities.
- Areas could be written as percents.
- Areas can not be negative.

Standard Normal curve

- The mean is 0.
- The standard deviation is 1.

Format of the table

- The table has 2 halves one for negative values

of z and one for positive values of z. - The left column tells the first decimal place for

the z the top row tells the second decimal place

for z. - We find the intersection of the row and column to

find the area to the LEFT of z.

Special notes

- For Z scores above 3.50, use the area of 0.9999
- For Z scores below -3.50, use the area of 0.0001

Reminder!

- Areas can never be negative.
- Z scores can be negative.

Area under the Standard Normal Distribution Curve

- 1. To the left of any z value
- Look up the z value in the table and use the area

given.

Bluman, Chapter 6

7

Area under the Standard Normal Distribution Curve

- 2. To the right of any z value
- Look up the z value and subtract the area from 1.

Bluman, Chapter 6

8

Area under the Standard Normal Distribution Curve

- 3. Between two z values
- Look up both z values and subtract the

corresponding areas.

Bluman, Chapter 6

9

Example 1

- Find the area to the left of z 2.25

Example 2

- Find the area to the right of z 1.50

Example 3

- Find the area between z -1.35 and z 2.15

Your Turn

- Find the area for each
- 1. area to the left of z -1.04
- 2. area to the right of z 1.07

Your turn continued

- area between z 0 and z 2.75
- area between z -1.00 and z 1.00

Finding z given area

- Make sure the diagram shows the area to the left

of the desired z score. - Look in the body of the chart for the closest

area, except for the special z scores. - Read the z score.

Example 4

- The area to the right of z is 0.0250

Example 5

- The area from the mean to a positive z is 0.1628

Example 6

- The area from some negative z to the mean is

0.4772

Your turn

- Find the z score for each
- 5 is to the left of z
- 2. the top 15

Your turn continued

- P15 Hint P15 means 15 is lower than x
- 88 of the area is between z and z

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