Standard Normal Distribution

Page 123

Standard Normal Distribution

• This is the Normal distribution with:– Mean of 0– Standard Deviation of 1

Standard Normal Distribution

• If a variable (x) has any Normal distribution with mean () and standard deviation (), the standardized variable has the standard Normal distribution.• THIS IS THE STANDARDIZED VARIABLE

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!

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

Example 3.7

Problem: Find the proportions of observations from the standard Normal distributions that are(a) Less than -1.25(b) Greater than 0.81

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 rowThe box that intersects these two is .1056Area less than -1.25 = .1056

Example 3.7 (cont.)

Example 3.7 (cont.)

Solution b: Find area to the right of z=0.81Locate 0.8 in the left-hand column of table ALocate the remaining digit 1 as .01 in the top rowThe entry where they intersect is .7910That is area to the LEFT of z=0.81To find area to the RIGHT of z=0.81, we use the area of 1 of the density curve and find the difference1-0.7910=0.2090

Example 3.7 (cont.)

Example

Problem: Find the proportion of observations from the standard Normal distribution that are between -1.25 and 0.81

Example (cont.)

Solution: =1-(0.506+0.2090)=1-0.3146=0.6854

3.2 Homework (cont.)

• Page 127-128• 3.28, 30, 32• Add these onto problems from yesterday– (3.22, 24, 26)