Download Penggunaan Distribusi Normal Normal Distribution Normal

Student Lecture Notes
Penggunaan
Distribusi Normal
Normal Distribution
1. ‘BellBell-Shaped’
Shaped’ &
Symmetrical
1. Menjelaskkan banyak proses acak
yang kontinu
X
3. ‘Middle Spread’
Spread’
adl 1.33 σ
Example: Binomial
4. Peubah Acak
mempunyai range tak
hingga
3. Dasar dari semua statistik inferensia
klasik
1
Mean
Median
Mode
2
Normal Distribution
Sifat yg penting
3
f(X)
2. Mean, Median,
Mode sama
2. Bisa digunakan untuk mendekati
peluang perubah acak diskrit
1
• Hampir separo “bobot/
weight”
weight” berada
dibawah mean (krn
symmetri)
• 68%
68% peluang berada
dlm 1 standard
deviation dari mean
• 95%
95% peluang berada
dlm 2 standard
deviations
• 99%
99% peluang berada
dlm 3 standard
deviations
Probability
Density Function
f(X)
f (x) =
µ +σ
µ − 3σ µ − 2σ µ − σ
µ + σ µ + 2σ µ + 3σ
x
σ
π
e
µ
X
Mean
Median
Mode
4
1
σ
2π
e
2
 11   xx −− µµ  2
−− 
 

 22   σσ

= Nilai Peubah acak (-∞ < x < ∞)
= Standard Deviation dari populasi
= 3.14159
= 2.71828
= Mean dari peubah acak x
Student Lecture Notes
Akibat dari Variasi
Parameter (µ & σ)
Notasi
X ~ N(µ
N(µ,σ)
Peubah Acak X mengikuti distribusi
Normal (N) dengan mean µ dan standard
deviation σ.
X ~ N(40,1)
X ~ N(10,5)
X ~ N(50,3)
5
f(X)
B
A
C
X
6
Normal Distribution
Probability
Peluang
dibawah
kurva!
d
Tak hingga tabel Normal
Tiap distribusi
memerlukan satu tabel.
?
P(c ≤ x ≤ d) = ∫? f (x) dx
c
f(X)
f(x)
c
7
2
d
X
x
8
Student Lecture Notes
Standardize the
Normal Distribution
Z=
Normal
Distribution
X −µ
σ
Contoh Standarisasi
Z is N(0,1)
Standardized
Normal Distribution
σ
σ=1
µ
µ= 0
X
X − µ 6.2 − 5
=
= .12
σ
10
Z=
Normal
Distribution
Standardized
Normal Distribution
σ = 10
Z
Hanya satu tabel!
9
3
σ=1
µ= 5 6.2 X
Mendapatkan
Peluangnya
Contoh
P(3.8 ≤ X ≤ 5)
Standardized Normal
Probability Table (Portion)
Z
.00
.01
Z=
σ=1
.02
0.0 .0000 .0040 .0080
µ= 0 .12 Z
10
X − µ 3.8 − 5
=
= − .12
σ
10
Normal
Distribution
Standardized
Normal Distribution
σ = 10
.0478
σ=1
0.1 .0398 .0438 .0478
0.2 .0793 .0832 .0871
.0478
µ= 0 .12 Z
0.3 .1179 .1217 .1255
11
Probabilities
3.8 µ = 5
12
X
-.12 µ = 0
Shaded area exaggerated
Z
Student Lecture Notes
4
Contoh
P(2.9 ≤ X ≤ 7.1)
Contoh
P(X
P(X ≥ 8)
X −− µµ 2.9 −− 5
==
== −−.21
σσ
10
X −− µµ 7.1 −− 5
Z ==
==
== .21
Standardized
σσ
10
Normal Distribution
Z ==
Normal
Distribution
Normal Distribution
σ = 10
Z=
X − µ 8−5
=
= .30
σ
10
Normal
Distribution
σ=1
Standardized
Normal Distribution
σ = 10
σ=1
.1664
.5000
2.9 5 7.1 X
13
-.21 0 .21
14
Contoh
P(7.1 ≤ X ≤ 8)
X −− µµ 7.1 −− 5
==
== .21
σσ
10
X −− µµ 8 −− 5
Z ==
==
== .30
Standardized
σσ
10
Normal Distribution
Z ==
Normal Distribution
σ = 10
σ=1
.1179
.0347
.0832
µ = 5 7.1 8 X
15
µ = 0 .21 .30 Z
Shaded area exaggerated
µ=5
Z
Shaded area exaggerated
Normal
Distribution
.3821
.1179
.0832 .0832
8 X
µ=0
Shaded area exaggerated
.30 Z