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Normal curve

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Make sure the diagram shows the area to the left of the desired z score. ... Example 6. The area from some negative z to the mean is 0.4772. Your turn ... – PowerPoint PPT presentation

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Title: Normal curve


1
Normal curve
2
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.

3
Standard Normal curve
  • The mean is 0.
  • The standard deviation is 1.

4
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.

5
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

6
Reminder!
  • Areas can never be negative.
  • Z scores can be negative.

7
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
8
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
9
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
10
Example 1
  • Find the area to the left of z 2.25

11
Example 2
  • Find the area to the right of z 1.50

12
Example 3
  • Find the area between z -1.35 and z 2.15

13
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

14
Your turn continued
  • area between z 0 and z 2.75
  • area between z -1.00 and z 1.00

15
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.

16
Example 4
  • The area to the right of z is 0.0250

17
Example 5
  • The area from the mean to a positive z is 0.1628

18
Example 6
  • The area from some negative z to the mean is
    0.4772

19
Your turn
  • Find the z score for each
  • 5 is to the left of z
  • 2. the top 15

20
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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