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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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For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

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