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  • #7464
    Qia
    Peserta

    Mohon bantuannya:))

    Hitunglah probabilitasnya bahwa suatu sampel random sebanyak 64 unit barang itu akan mempunyai berat rata-rata:
    a. Antara 39,9 dan 41,1 kg
    b. Antara 40,2 dan 40,6 kg
    c. Kurang dari 40,5 kg
    d. Lebih dari 41,2 kg

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  • #7467
    StatistikaA
    Peserta

    Diketahui \(\mu = 40\text{,}6\) , \(n=64\) , dan \(\sigma = 2\text{,}6\)
    Pertanyaan diatas dapat diselesaikan menggunakan Tabel Z
    \[\begin{aligned}Z&=\frac{X-\mu}{\sigma }\end{aligned}\]
    A. \[\begin{aligned}P(39\text{,}9<X<41\text{,}1)&=P(X<41\text{,}1)-P(X<39\text{,}9)\\&=P\left(Z<\frac{41\text{,}1-40\text{,}6}{2\text{,}6}\right)-P\left(Z<\frac{39\text{,}9-40\text{,}6}{2\text{,}6}\right)\\&=P(Z<0\text{,}19)-P(Z<-0\text{,}27)\\&=0\text{,}5753-0\text{,}3936\\&=0\text{,}1817\end{aligned}\]
    B.\[\begin{aligned}P(40\text{,}2<X<40\text{,}6)&=P(X<40\text{,}6)-P(X<40\text{,}2)\\&=P\left(Z<\frac{40\text{,}6-40\text{,}6}{2\text{,}6}\right)-P\left(Z<\frac{40\text{,}2-40\text{,}6}{2\text{,}6}\right)\\&=P(Z<0)-P(Z<-0\text{,}15)\\&=0\text{,}5-0\text{,}4404\\&=0\text{,}0596\end{aligned}\]
    C.\[\begin{aligned}P(X<40\text{,}5)&=P\left(Z<\frac{40\text{,}5-40\text{,}6}{2\text{,}6}\right)\\&=P(Z<-0\text{,}04)\\&=0\text{,}4840\end{aligned}\]
    D.\[\begin{aligned}P(X>41\text{,}2)&=1-P(Z<41\text{,}2)\\&=1-P\left(Z<\frac{41\text{,}2-40\text{,}6}{2\text{,}6}\right)\\&=1-P(Z<0\text{,}23)\\&=1-0\text{,}5910\\&=0\text{,}409\end{aligned}\]

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