pert-4 distribusi normal
DESCRIPTION
Statistika PenelitianTRANSCRIPT
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DISTRIBUSI NORMAL
BAB 8
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KARAKTERISTIK DISTRIBUSI KURVA NORMAL
1. Kurva berbentuk genta (= Md= Mo)2. Kurva berbentuk simetris3. Kurva normal berbentuk asimptotis4. Kurva mencapai puncak pada saat X= 5. Luas daerah di bawah kurva adalah 1; ½ di sisi kanan
nilai tengah dan ½ di sisi kiri.
DISTRIBUSI NORMAL
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JENIS-JENIS DISTRIBUSI NORMAL
0
1
2
3
4
5
6
7
8
9
10
m
Mesokurtic Platykurtic Leptokurtic
Distribusi kurva normal dengan sama dan berbeda
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DEFINISI KURVA NORMAL
Bila X suatu variabel random normal dengan nilai tengah , dan standar deviasi , maka persamaan kurva normalnya adalah:
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Grafik kurva normal :
P(x≤) = 0,5P(x) = 0,5Luas kurva normal :
0,50,5
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Menentukan peluang harga x antara a dan b
Luas kurva normal antara x=a & x=b = probabilitas x terletak antara a dan
b
a b x
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TRANSFORMASI DARI NILAI X KE Z
Transformasi dari X ke Z
x z
Di mana nilai Z:
Z = X -
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Z > 0 jika x > Z < 0 jika x < Simetri : P(0 ≤ Z ≤ b) = P(-b ≤ Z ≤ 0)
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Contoh :1. Diketahui data berdistribusi normal dengan
mean = 55 dan deviasi standar = 15a) P(55≤x≤75) =
=
= P(0≤Z≤1,33) = 0,4082 (Tabel III)
Atau
Tabel III A =
0,4082
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2.
3.
4.
5.
)8060( xP
)6040( xP
)40( xP
)85( xP
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b) P(60≤x≤80) == P(0,33≤Z≤1,67)= P(0≤Z≤1,67) – P(0≤Z≤0,33)= 0,4525 – 0,1293 = 0,3232
Z1 = = 0,33 B = 0,1293
Z2 = = 1,67 A = 0,4525C = A – B = 0,3232
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c) P(40≤x≤60)= A + B
= = P(-1,00≤Z≤0,33) = P(-1,00≤Z≤0) +
P(0≤Z≤0,33) = 0,3412 + 0,1293 = 0,4705 Atau : Z1 = = -1,00 A = 0,3412 Z2 = = 0,33 B = 0,1293
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d) P(x ≤ 40) = 0,5 – A
= 0,5 – 0,3412 = 0,1588
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e. P(x ≥ 85)
f. P(x ≤ 85) = 0,5 + A= 0,5 + 0,4772= 0,9772
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soal
1. Berat bayi yang baru lahir rata-rata 3.750 gram dengan simpangan baku 325 gram. Jika berat bayi berdistribusi normal, maka tentukan ada:
a. Berapa persen bayi yg beratnya lebih dari atau sama dg 4.500 gram?
b. Berapa bayi yang beratnya antara 3.500 gram dan 4.500 gram, jika semuanya ada 10.000 bayi?
c. Berapa bayi yg beratnya lebih kecil atau sama dengan 4.000 gram jika semuanya ada 10.000 bayi?
d. Berapa bayi yang beratnya 4.250 gram jika semuanya ada 5.000 bayi?