Chap 5-1 Bab 5 Distribusi Normal
Chap 5-1
Bab 5Distribusi Normal
Chap 5-2
Topik
distribusi normal
distribusi normal standar
Chap 5-3
Distribusi Probabilitas Kontinu
variabel random kontinuValues from interval of numbersAbsence of gaps
distribution probabilitas kontinuDistribution of continuous random variable
Most important continuous probability distribution
distribusi normal
Chap 5-4
Distribusi Normal
“Bell shaped”SymmetricalMean, median and mode are equalInterquartile rangeequals 1.33 σRandom variablehas infinite range
Mean Median Mode
X
f(X)
µ
Chap 5-5
Model Matematika
( )( )
( )
( )
212
2
12
: density of random variable 3.14159; 2.71828
: population mean: population standard deviation: value of random variable
Xf X e
f X Xe
X X
µσ
πσ
πµσ
2− −=
= =
−∞ < < ∞
Chap 5-6
Beberapa Distribusi Normal
distribusi normal dengan parameters
σ and µ, berbeda
Chap 5-7
Menentukan Nilai Probabilitas
Probability is the area under the curve!
c dX
f(X)
( ) ?P c X d≤ ≤ =
Chap 5-8
Tabel yang digunakan?
An infinite number of normal distributions means an infinite number of tables to look up!
Chap 5-9
Distribution Normal Standar
Z .00 .01
0.0 .5000 .5040 .5080
.5398 .5438
0.2 .5793 .5832 .5871
0.3 .6179 .6217 .6255
.5478.02
0.1 .5478
Cumulative Standardized Normal Distribution Table (Portion)
Probabilities
Shaded Area Exaggerated
0 1Z Zµ σ= =
Z = 0.120
Only One Table is Needed
Chap 5-10
Contoh6.2 5 0.12
10XZ µσ− −
= = =
Normal Distribution Standardized Normal Distribution
Shaded Area Exaggerated
10σ = 1Zσ =
5µ =6.2 X Z0Zµ =
0.12
Chap 5-11
Contoh( )2.9 7.1 .1664P X≤ ≤ =2.9 5 7.1 5.21 .21
10 10X XZ Zµ µσ σ− − − −
= = = − = = =
Normal Distribution Standardized Normal Distribution
Shaded Area Exaggerated
10σ = 1Zσ =
5µ =7.1 X Z0Zµ =
0.212.9 0.21−
.0832.0832
Chap 5-12
Contoh:( )2.9 7.1 .1664P X≤ ≤ =
(continued)
Z .00 .01
0.0 .5000 .5040 .5080
.5398 .5438
0.2 .5793 .5832 .5871
0.3 .6179 .6217 .6255
.5832.02
0.1 .5478
Cumulative Standardized Normal Distribution Table (Portion)
Shaded Area Exaggerated
0 1Z Zµ σ= =
Z = 0.210
Chap 5-13
Contoh:( )2.9 7.1 .1664P X≤ ≤ =
(continued)
Z .00 .01
-03 .3821 .3783 .3745
.4207 .4168
-0.1.4602 .4562 .4522
0.0 .5000 .4960 .4920
.4168.02
-02 .4129
Cumulative Standardized Normal Distribution Table (Portion)
Shaded Area Exaggerated
0 1Z Zµ σ= =
Z = -0.210
Chap 5-14
Contoh:( )8 .3821P X ≥ =
8 5 .3010
XZ µσ− −
= = =
Normal Distribution Standardized Normal Distribution
Shaded Area Exaggerated
10σ = 1Zσ =
5µ =8 X Z0Zµ =
0.30
.3821
Chap 5-15
Contoh:( )8 .3821P X ≥ =
(continued)
Cumulative Standardized Normal Distribution Table (Portion) 0 1Z Zµ σ= =
Z .00 .01
0.0 .5000 .5040 .5080
.5398 .5438
0.2 .5793 .5832 .5871
0.3 .6179 .6217 .6255
.02
0.1 .5478
.6179
Shaded Area Exaggerated
Z = 0.300
Chap 5-16
Mengetahui nilai Zpada Probabilitas tertentu
Cumulative Standardized Normal Distribution Table
(Portion)What is Z Given Probability = 0.1217 ?
Z .00 0.2
0.0 .5000 .5040 .5080
0.1 .5398 .5438 .5478
0.2 .5793 .5832 .5871
.6179 .6255
.01
0.3
.6217
Shaded Area Exaggerated
.6217
0 1Z Zµ σ= =
.31Z =0
Chap 5-17
Nilai Xuntuk mengetahui Probabilitas
( )( )5 .30 10 8X Zµ σ= + = + =
Normal Distribution Standardized Normal Distribution
10σ = 1Zσ =
5µ = ? X Z0Zµ =0.30
.3821.1179
Chap 5-18
Assessing Normality(continued)
Normal Probability Plot for Normal Distribution
3060
90
-2 -1 0 1 2Z
X
Look for Straight Line!
Chap 5-19
Normal Probability Plot
Left-Skewed Right-Skewed
30
60
90
-2 -1 0 1 2Z
X30
60
90
-2 -1 0 1 2Z
X
Rectangular U-Shaped
30
60
90
-2 -1 0 1 2Z
X30
60
90
-2 -1 0 1 2Z
X
Chap 5-20
Larger sample size
Smaller sample size
P(X)
µ X
Chap 5-21
Populasi NormalPopulation Distribution
Sampling Distributions
Central Tendency
X50Xµ =
45X
nσ==
162.5X
nσ==
50µ =
10σ =
Xµ µ=
Variation
X nσσ =
Sampling with Replacement
Chap 5-22
Populasitidak Normal
Central Tendency
Variation
Sampling with Replacement
Population Distribution
Sampling Distributions
Xµ µ=
X nσσ =
X50Xµ =
45X
nσ==
301.8X
nσ==
50µ =
10σ =
Chap 5-23
Central Limit Theorem
As sample size gets large enough…
the sampling distribution becomes almost normal regardless of shape of population
X
Chap 5-24
Contoh:( )
8 =2 25
7.8 8.2 ?
n
P X
µ σ= =
< < =
( )
( )
7.8 8 8.2 87.8 8.22 / 25 2 / 25
.5 .5 .3830
X
X
XP X P
P Z
µσ
⎛ ⎞−− −< < = < <⎜ ⎟
⎝ ⎠= − < < =
Sampling Distribution Standardized Normal Distribution2 .4
25Xσ = = 1Zσ =
8Xµ =8.2 Z
0Zµ =0.57.8 0.5−
.1915
X