Post on 01-Apr-2015
transcript
Chapter 6: Probability
Sample Population
Inferential Statistics
Probability
Probability of A
=Number of outcomes classified as A
Total number of possible outcomes
Probability is Proportion
• Coin tosses -- p (heads) = ?
• Cards
• p (King of Hearts) = ?
• p (ace) = ?
• p (red ace) = ?
6, 6, 7, 7, 7, 7, 8, 8, 8, 9
x f
9 1
8 3
7 4
6 2
Random Sample
1. Each individual in the population has an equal chance of being selected.
2. If more than one individual is selected, there must be constant probability for each and every selection.
Biased Sample
1, 1, 2, 3, 3, 4, 4, 4, 5, 6
x f
6 1
5 1
4 3
3 2
2 1
1 2
1 2 3 4 5 6 7 8
1
2
3
X
freq
uenc
y
1 2 3 4 5 6 7 8
1
2
3
X
freq
uenc
y
µ X
13.59%
µ
z-2 -1 0 +1 +2
34.13%
13.59%
2.28%
= 6
µX68 74 80
6.5 (a)
µ
z68 74 80
(b)
0 +2.00
z-2 -1 0 +1 +2-3 +3
(A)
z
(B)
Proportion in Body
(C)
Proportion in Tail
0.00 0.5000 0.5000
0.01 0.5040 0.4960
0.02 0.5080 0.4920
0.03 0.5120 0.4880
0.21 0.5832 0.4168
0.22 0.5871 0.4129
0.23 0.5910 0.4090
0.24 0.5948 0.4052
0.25 0.5987 0.4013
0.26 0.6026 0.3974
0.27 0.6064 0.3936
0.28 0.6103 0.3897
0.29 0.6141 0.3859
Mean z
zMean
CC
B
(c)
z0-.5µ
(a)
0 1.0z
µ
(b)
z0 1.5µ
z
(a)
µ-0.40 0 1.25
µ
z
(b)
0.350 1.40
X Z
Probability
z-score formula
Unit normal table
= 100
X
µ
500 650
z0 1.50
= 100
X
µ
500 700
z0 2.00
600
1.00
= 100
Xµ = 500
z0 1.04
Top 15%
Xµ = 100
z0 1.40
= 10
114
Xµ = 100
z0-0.80
= 10
92
Xµ = 60
= 5
P = 0.3400or 34%
25% 25% 25% 25%z
Quartiles0 +0.67-0.67
Q1 Q2 Q3
0.50
0.25
00 1 2
Pro
babi
lity
Number of heads in two coin tosses
0 1 2 3 4
0.375
0.250
0.125
Pro
babi
lity
(a)
0 1 2 3 4 5 6
Pro
babi
lity
0.2500
0.1875
0.1250
0. 0625
(b)
Number of Heads in six coin tosses
Number of Heads in four coin tosses
The Relationship Between the Binomial Distribution and the Normal Distribution
X0 1 2 3 4 5 6 7 8 9 10