1. NORMAL PROBABILITY DISTRIBUTIONS
The Most Important Probability Distribution in Statistics
Total area =1; symmetric around µ

2. The effects of m and s X 3 6 9 12  µ = 3 and  = 1
How does the standard deviation affect the shape of f(x)?
The effects of m and s
s= 2
s =3
s =4
How does the expected value affect the location of f(x)?
m = 10
m = 11
m = 12 X 8 3 6 9 12 
µ = 3 and  = 1

3. µ = 3 and  = 1  X 3 6 9 12
µ = 6 and  = 1  X 3 6 9 12

4. X 8 3 6 9 12 
µ = 6 and  = 2 X 8 3 6 9 12 
µ = 6 and  = 1

5. P(6 < X < 8)
µ = 6 and  = 2 X 3 6 9 12 X
Probability = area under the density curve
P(6 < X < 8 ) = area under the density curve between 6 and 8. 6 8

6. Standardizing

7. Standard Normal DistributionZ 1 2 3 -1 -2 -3 .5 .5 .5
0.452

8. P(z  -1.85)
-1.85 A1 A2 z
-1.18
2.73
P(-1.18  z  2.73)