pemakaian distribusi normal
DESCRIPTION
distribusi normalTRANSCRIPT
Student Lecture Notes 1
11
Penggunaan Penggunaan Distribusi NormalDistribusi Normal
1.1. Menjelaskkan banyak proses acak Menjelaskkan banyak proses acak yang kontinuyang kontinu
2.2. Bisa digunakan untuk mendekati Bisa digunakan untuk mendekati peluang perubah acak diskritpeluang perubah acak diskrit�� Example: BinomialExample: Binomial
3.3. Dasar dari semua statistik inferensia Dasar dari semua statistik inferensia klasikklasik
22
Normal DistributionNormal Distribution
1.1. ‘‘BellBell--ShapedShaped’’ & & SymmetricalSymmetrical
2.2. Mean, Median, Mean, Median, Mode Mode samasama
3.3. ‘‘Middle SpreadMiddle Spread’’adladl 1.33 1.33 σσ
4.4. Peubah Acak Peubah Acak mempunyai range tak mempunyai range tak hinggahingga
Mean Mean Median Median ModeMode
X
f(X)
33
Normal Distribution Normal Distribution Sifat yg pentingSifat yg penting
•• Hampir separo Hampir separo ““bobot/ bobot/ weightweight”” berada berada dibawah meandibawah mean (krn(krnsymmetri)symmetri)
•• 6868% % peluang berada peluang berada dlmdlm 1 standard 1 standard deviation deviation daridari mean mean
•• 9595% % peluang berada peluang berada dlmdlm 2 standard 2 standard deviationsdeviations
•• 9999% % peluang berada peluang berada dlmdlm 3 standard 3 standard deviations deviations
Mean Mean Median Median ModeMode
X
f(X)
σµ +
σµ − σµ +σµ 2− σµ 2+ σµ 3+σµ 3−
44
Probability Probability Density FunctionDensity Function
2
2
1
e2
1)(
−
−= σ
µ
πσ
x
xf
2
2
1
e2
1)(
−
−= σ
µ
πσ
x
xf
xx == Nilai Peubah acakNilai Peubah acak ((--∞∞ < < xx < < ∞∞))σσ == StandardStandard DeviationDeviation dari populasidari populasiππ == 3.141593.14159e = 2.71828e = 2.71828µµ == Mean Mean dari peubah acakdari peubah acak xx
Student Lecture Notes 2
55
NotasiNotasi
X X ~~ N(N(µµ,,σσ))
Peubah AcakPeubah Acak X mengikuti distribusi X mengikuti distribusi NormalNormal (N) (N) dengan meandengan mean µµ dandan standard standard deviation deviation σσ..
X X ~~ N(40,1)N(40,1)
X X ~~ N(10,5)N(10,5)
X X ~~ N(50,3)N(50,3)
66
Akibat dari Variasi Akibat dari Variasi ParameterParameter ((µµµµµµµµ & & σσσσσσσσ))
X
f(X)
CA
B
77
Normal Distribution Normal Distribution ProbabilityProbability
?)()( dxxfdxcPd
c∫=≤≤
c dx
f(x)
c dx
f(x)
Peluang Peluang dibawah dibawah kurva!kurva!
??
88
X
f(X)
X
f(X)
Tak hingga tabel NormalTak hingga tabel Normal
Tiap distribusi Tiap distribusi memerlukan satu tabel.memerlukan satu tabel.
Student Lecture Notes 3
99
Standardize theStandardize theNormal DistributionNormal Distribution
Xµµµµ
σσσσ
Xµµµµ
σσσσ
Hanya satu tabel!Hanya satu tabel!
Normal DistributionNormal Distribution
µµµµ = 0
σσσσ = 1
Zµµµµ = 0
σσσσ = 1
Z
ZX==== −−−− µµµµ
σσσσZ
X==== −−−− µµµµσσσσ Standardized
Normal DistributionStandardized
Normal Distribution
Z is N(0,1)Z is N(0,1)
1010
Contoh StandarisasiContoh Standarisasi
Xµµµµ= 5
σσσσ = 10
6.2 Xµµµµ= 5
σσσσ = 10
6.2
Normal DistributionNormal Distribution
ZX==== −−−− ==== −−−− ====µµµµ
σσσσ6 2 5
1012
..Z
X==== −−−− ==== −−−− ====µµµµσσσσ
6 2 510
12.
.
Zµµµµ= 0
σσσσ = 1
.12 Zµµµµ= 0
σσσσ = 1
.12
Standardized Normal Distribution
Standardized Normal Distribution
1111
Zµµµµ= 0
σσσσ = 1
.12 Zµµµµ= 0
σσσσ = 1
.12
Z .00 .01
0.0 .0000 .0040 .0080
.0398 .0438
0.2 .0793 .0832 .0871
0.3 .1179 .1217 .1255
Z .00 .01
0.0 .0000 .0040 .0080
.0398 .0438
0.2 .0793 .0832 .0871
0.3 .1179 .1217 .1255
Mendapatkan Mendapatkan PeluangnyaPeluangnya
.0478.0478.0478
.02.02
0.10.1 .0478
Standardized Normal Probability Table (Portion)Standardized Normal Standardized Normal Probability Table (Portion)Probability Table (Portion)
ProbabilitiesProbabilitiesProbabilities1212
ContohContohP(3.8P(3.8 ≤≤≤≤≤≤≤≤ XX ≤≤≤≤≤≤≤≤ 5)5)
Xµ µ µ µ = 5
σσσσ = 10
3.8 Xµ µ µ µ = 5
σσσσ = 10
3.8
Normal DistributionNormal Normal DistributionDistribution
ZX==== −−−− ==== −−−− ==== −−−−µµµµ
σσσσ3 8 5
1012
..Z
X==== −−−− ==== −−−− ==== −−−−µµµµσσσσ
3 8 510
12.
.
Zµµµµ = 0
σσσσ = 1
-.12 Zµµµµ = 0
σσσσ = 1
-.12
.0478.0478
Standardized Normal Distribution
Standardized Standardized Normal DistributionNormal Distribution
Shaded area exaggeratedShaded area exaggeratedShaded area exaggerated
Student Lecture Notes 4
1313
ContohContohP(2.9 P(2.9 ≤≤≤≤≤≤≤≤ XX ≤≤≤≤≤≤≤≤ 7.1) 7.1)
5
σσσσ = 10
2.9 7.1 X5
σσσσ = 10
2.9 7.1 X
Normal DistributionNormal Normal DistributionDistribution
ZX
ZX
====−−−− ====
−−−− ==== −−−−
====−−−− ====
−−−− ====
µµµµσσσσ
µµµµσσσσ
2 9 510
21
7 1 510
21
..
..
ZX
ZX
====−−−− ====
−−−− ==== −−−−
====−−−− ====
−−−− ====
µµµµσσσσ
µµµµσσσσ
2 9 510
21
7 1 510
21
..
..
0
σσσσ = 1
-.21 Z.210
σσσσ = 1
-.21 Z.21
.1664.1664.1664
.0832.0832.0832.0832
Standardized Normal Distribution
Standardized Standardized Normal DistributionNormal Distribution
Shaded area exaggeratedShaded area exaggeratedShaded area exaggerated 1414
Contoh Contoh P(P(XX ≥≥≥≥≥≥≥≥ 8)8)
Xµµµµ = 5
σσσσ = 10
8 Xµµµµ = 5
σσσσ = 10
8
Normal DistributionNormal Normal DistributionDistribution
Standardized Normal Distribution
Standardized Standardized Normal DistributionNormal Distribution
ZX==== −−−− ==== −−−− ====µµµµ
σσσσ8 510
30.ZX==== −−−− ==== −−−− ====µµµµ
σσσσ8 510
30.
Zµµµµ = 0
σσσσ = 1
.30 Zµµµµ = 0
σσσσ = 1
.30
.1179.1179.1179
.5000.5000.3821.3821.3821
Shaded area exaggeratedShaded area exaggeratedShaded area exaggerated
1515
Contoh Contoh P(7.1 P(7.1 ≤≤≤≤≤≤≤≤ XX ≤≤≤≤≤≤≤≤ 8)8)
µµµµ = 5
σσσσ = 10
87.1 Xµµµµ = 5
σσσσ = 10
87.1 X
Normal DistributionNormal Normal DistributionDistribution
ZX
ZX
====−−−− ====
−−−− ====
====−−−− ====
−−−− ====
µµµµσσσσ
µµµµσσσσ
7 1 510
21
8 510
30
..
.
ZX
ZX
====−−−− ====
−−−− ====
====−−−− ====
−−−− ====
µµµµσσσσ
µµµµσσσσ
7 1 510
21
8 510
30
..
.
µµµµ = 0
σσσσ = 1
.30 Z.21µµµµ = 0
σσσσ = 1
.30 Z.21
.0832.0832
.1179.1179 .0347.0347.0347
Standardized Normal Distribution
Standardized Standardized Normal DistributionNormal Distribution
Shaded area exaggeratedShaded area exaggeratedShaded area exaggerated