Distribusi Normal

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    Topik Pertanyaan
  • #8996

    Z = upah karyawan per bulan dalam ribuan rupiah, mengikuti fungsi normal dengan rata-rata sebesar Rp.75 ribu dan deviasi standar Rp.15 ribu. Saudara bertemu dengan salah seorang karyawan tersebut.
    Hitung P (X >= 60), P (60<=X<=80), P (X >= 65), P (X <= 85) , dan P (X <= 90)

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    Jawaban
  • #8997
    StatistikaA
    Peserta

    Diketahui \(\mu = 75\) ribu , dan \(\sigma = 15\) ribu
    Pertanyaan diatas dapat diselesaikan menggunakan Tabel Z
    \[\begin{aligned}Z&=\frac{X-\mu}{\sigma }\end{aligned}\]
    1. \[\begin{aligned}P(X\geq60)&=1-P\left(Z\leq\frac{60-75}{15}\right)\\&=1-P(Z\leq-1)\\&=1-0\text{,}1587\\&=0\text{,}8413\end{aligned}\]
    2. \[\begin{aligned}P(60<X<80)&=P(X<80)-P(X<60)\\&=P\left(Z<\frac{80-75}{15}\right)-P\left(Z<\frac{60-75}{15}\right)\\&=P(Z<0\text{,}33)-P(Z<-1)\\&=0\text{,}6293-0\text{,}1587\\&=0\text{,}4706\end{aligned}\]
    3. \[\begin{aligned}P(X\geq65)&=1-P\left(Z\leq\frac{65-75}{15}\right)\\&=1-P(Z\leq-0\text{,}67)\\&=1-0\text{,}2514\\&=0\text{,}7486\end{aligned}\]
    4. \[\begin{aligned}P(X\leq85)&=P\left(Z\leq\frac{85-75}{15}\right)\\&=P(Z\leq0\text{,}67)\\&=0\text{,}7486\end{aligned}\]
    5.\[\begin{aligned}P(X\leq90)&=P\left(Z\leq\frac{90-75}{15}\right)\\&=P(Z\leq 1)\\&=0\text{,}8413\end{aligned}\]

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