Distribusi normal

• Pencipta
  Topik Pertanyaan
• Tanggal 30-11-2020 jam 17:32 #8709
  Mrs Hwanggg

  Peserta

  Diketahui suatu distribusi normal (X) dengan µ = 200 dan σ2 = 100. Hitunglah:
  a. Luas daerah dimana x < 214
  b. Luas daerah dimana x > 179
  c. Luas daerah 188 < x < 206

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  Topik Pertanyaan

Jawaban :

• Penulis
  Jawaban
• Tanggal 30-11-2020 jam 20:19 #8714
  StatistikaA

  Peserta

  Diketahui \(\mu = 200\) , dan \(\sigma = 10\)
  Pertanyaan diatas dapat diselesaikan menggunakan Tabel Z
  A.\[\begin{aligned}P(X<214)&=P(Z<214)\\&=P\left(Z<\frac{214-200}{10}\right)\\&=P\left(Z<1\text{,}4\right)\\&=0\text{,}9192\end{aligned}\]
  B.\(\begin{aligned}P(X>179)\end{aligned}\)
  \[\begin{aligned}P(X>179)&=1-P(Z<179)\\&=1-P\left(Z<\frac{179-200}{10}\right)\\&=1-P\left(Z<-2\text{,}1\right)\\&=0\text{,}9821\end{aligned}\]
  C. \[\begin{aligned}P(188<X<206)&=P(X<206)-P(X<188)\\&=P\left(Z<\frac{206-200}{10}\right)-P\left(Z<\frac{188-200}{10}\right)\\&=P(Z<0\text{,}6)-P(Z<-1\text{,}2)\\&=0\text{,}257-0\text{,}1151\\&=0\text{,}6106\end{aligned}\]

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