1. Standard Normal Distribution
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2. Standard Normal Distribution
This is the Normal distribution with:
Mean of 0
Standard Deviation of 1

3. Standard Normal Distribution
If a variable (x) has any Normal distribution with mean (𝜇) and standard deviation (𝜎), the standardized variable has the standard Normal distribution.
𝑧= 𝑥−𝜇 𝜎 THIS IS THE STANDARDIZED VARIABLE

4. The standard Normal table
All Normal distributions are the same when we standardize them
We can find areas under any Normal curve from a single table.
Table A (standard Normal table)
Located at the back of the book!

5. Standard Normal Table (Table A)
Table of areas under the standard Normal curve.
Table entry for each value z is the:
Area under the curve
To the left of z

6. Example 3.7
Problem: Find the proportions of observations from the standard Normal distributions that are
Less than -1.25
Greater than 0.81

7. Example 3.7 (cont.)
Solution a: To find area to left of -1.25, Locate -1.2 in the left-hand column of table A.
Then locate the remaining digit 5 as.05 in the top row
The box that intersects these two is .1056
Area less than =

8. Example 3.7 (cont.)

9. Example 3.7 (cont.)
Solution b: Find area to the right of z=0.81 Locate 0.8 in the left-hand column of table A Locate the remaining digit 1 as .01 in the top row The entry where they intersect is That is area to the LEFT of z=0.81 To find area to the RIGHT of z=0.81, we use the area of 1 of the density curve and find the difference =0.2090

10. Example 3.7 (cont.)

11. Example
Problem: Find the proportion of observations from the standard Normal distribution that are between and 0.81

12. Example (cont.)
Solution: =1-( ) = =0.6854

13. 3.2 Homework (cont.)
Page
3.28, 30, 32
Add these onto problems from yesterday
(3.22, 24, 26)