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Bab 5
Distribusi Normal
© 2002 Prentice-Hall, Inc.
Chap 5-1
Topik

distribusi normal

distribusi normal standar
© 2002 Prentice-Hall, Inc.
Chap 5-2
Distribusi Probabilitas Kontinu

variabel random kontinu



distribution probabilitas kontinu


Values from interval of numbers
Absence of gaps
Distribution of continuous random variable
Most important continuous probability
distribution

distribusi normal
© 2002 Prentice-Hall, Inc.
Chap 5-3
Distribusi Normal





“Bell shaped”
Symmetrical
Mean, median and
mode are equal
Interquartile range
equals 1.33 s
Random variable
has infinite range
© 2002 Prentice-Hall, Inc.
f(X)

X
Mean
Median
Mode
Chap 5-4
Model Matematika
f X  
1

e
1
2s
2
X





2s 2
f  X  : density of random variable X
  3.14159;
e  2.71828
 : population mean
s : population standard deviation
X : value of random variable    X   
© 2002 Prentice-Hall, Inc.
Chap 5-5
Beberapa Distribusi Normal
distribusi normal dengan parameters
© 2002 Prentice-Hall, Inc.
s and , berbeda
Chap 5-6
Menentukan Nilai Probabilitas
Probability is
the area under
the curve!
P c  X  d   ?
f(X)
c
© 2002 Prentice-Hall, Inc.
d
X
Chap 5-7
Tabel yang digunakan?
An infinite number of normal distributions
means an infinite number of tables to look up!
© 2002 Prentice-Hall, Inc.
Chap 5-8
Distribution Normal Standar
Cumulative Standardized Normal
Distribution Table (Portion)
Z
.00
.01
Z  0
sZ 1
.02
.5478
0.0 .5000 .5040 .5080
Shaded Area
Exaggerated
0.1 .5398 .5438 .5478
0.2 .5793 .5832 .5871
Probabilities
0.3 .6179 .6217 .6255
© 2002 Prentice-Hall, Inc.
0
Z = 0.12
Only One Table is Needed
Chap 5-9
Contoh
Z
X 
s
6.2  5

 0.12
10
Standardized
Normal Distribution
Normal Distribution
s  10
 5
© 2002 Prentice-Hall, Inc.
sZ 1
6.2
X
Shaded Area Exaggerated
Z  0
0.12
Z
Chap 5-10
Contoh
P  2.9  X  7.1  .1664
Z
X 
s
2.9  5

 .21
10
Z
X 
s
7.1  5

 .21
10
Standardized
Normal Distribution
Normal Distribution
s  10
.0832
sZ 1
.0832
2.9
 5
© 2002 Prentice-Hall, Inc.
7.1
X
0.21
Shaded Area Exaggerated
Z  0
0.21
Z
Chap 5-11
Contoh:
P  2.9  X  7.1  .1664(continued)
Cumulative Standardized Normal
Distribution Table (Portion)
Z
.00
.01
Z  0
sZ 1
.02
.5832
0.0 .5000 .5040 .5080
Shaded Area
Exaggerated
0.1 .5398 .5438 .5478
0.2 .5793 .5832 .5871
0.3 .6179 .6217 .6255
© 2002 Prentice-Hall, Inc.
0
Z = 0.21
Chap 5-12
Contoh:
P  2.9  X  7.1  .1664(continued)
Cumulative Standardized Normal
Distribution Table (Portion)
Z
.00
.01
.02
Z  0
sZ 1
.4168
-03 .3821 .3783 .3745
Shaded Area
Exaggerated
-02 .4207 .4168 .4129
-0.1 .4602 .4562 .4522
0.0 .5000 .4960 .4920
© 2002 Prentice-Hall, Inc.
0
Z = -0.21
Chap 5-13
Contoh:
P  X  8  .3821
Z
X 
s
85

 .30
10
Standardized
Normal Distribution
Normal Distribution
s  10
sZ 1
.3821
 5
© 2002 Prentice-Hall, Inc.
8
X
Shaded Area Exaggerated
Z  0
0.30
Z
Chap 5-14
Contoh:
P  X  8  .3821
Cumulative Standardized Normal
Distribution Table (Portion)
Z
.00
.01
Z  0
(continued)
sZ 1
.02
.6179
0.0 .5000 .5040 .5080
Shaded Area
Exaggerated
0.1 .5398 .5438 .5478
0.2 .5793 .5832 .5871
0.3 .6179 .6217 .6255
© 2002 Prentice-Hall, Inc.
0
Z = 0.30
Chap 5-15
Mengetahui nilai Z
pada Probabilitas tertentu
What is Z Given
Probability = 0.1217 ?
Z  0
sZ 1
Cumulative Standardized
Normal Distribution Table
(Portion)
Z
.00
.01
0.2
0.0 .5000 .5040 .5080
.6217
0.1 .5398 .5438 .5478
0.2 .5793 .5832 .5871
Shaded Area
Exaggerated
© 2002 Prentice-Hall, Inc.
0
Z  .31
0.3 .6179 .6217 .6255
Chap 5-16
Nilai X
untuk mengetahui Probabilitas
Standardized
Normal Distribution
Normal Distribution
s  10
sZ 1
.1179
.3821
 5
?
X
Z  0
0.30
Z
X    Zs  5  .3010  8
© 2002 Prentice-Hall, Inc.
Chap 5-17
Assessing Normality
(continued)
Normal Probability Plot for Normal
Distribution
90
X 60
Z
30
-2 -1 0 1 2
© 2002 Prentice-Hall, Inc.
Look for Straight Line!
Chap 5-18
Normal Probability Plot
Left-Skewed
Right-Skewed
90
90
X 60
X 60
Z
30
-2 -1 0 1 2
-2 -1 0 1 2
Rectangular
U-Shaped
90
90
X 60
X 60
Z
30
-2 -1 0 1 2
© 2002 Prentice-Hall, Inc.
Z
30
Z
30
-2 -1 0 1 2
Chap 5-19
Larger
sample size
P(X)
Smaller
sample size

© 2002 Prentice-Hall, Inc.
X
Chap 5-20
Populasi Normal
Population Distribution
Central Tendency
X  
Variation
sX 
s
n
Sampling with
Replacement
© 2002 Prentice-Hall, Inc.
s  10
  50
Sampling Distributions
n4
n  16
sX 5
s X  2.5
 X  50
X
Chap 5-21
Populasi
tidak Normal
Population Distribution
Central Tendency
X  
Variation
sX 
s
n
Sampling with
Replacement
© 2002 Prentice-Hall, Inc.
s  10
  50
Sampling Distributions
n4
n  30
sX 5
s X  1.8
 X  50
X
Chap 5-22
Central Limit Theorem
As sample
size gets
large
enough…
the
sampling
distribution
becomes
almost
normal
regardless
of shape of
population
X
© 2002 Prentice-Hall, Inc.
Chap 5-23
Contoh:
 8
s =2
n  25
P  7.8  X  8.2   ?
 7.8  8 X   X 8.2  8 
P  7.8  X  8.2   P 



sX
2 / 25 
 2 / 25
 P  .5  Z  .5  .3830
Standardized
Normal Distribution
Sampling Distribution
2
sX 
 .4
25
sZ 1
.1915
7.8
© 2002 Prentice-Hall, Inc.
8.2
X  8
X
0.5
Z  0
0.5
Z
Chap 5-24