Menghitung luas kurva distribusi normal

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  • #5230
    aisyah

    Jika kita punya kurve normal dengan μ =100, dan σ = 20, maka hitunglah luas kurva normal antara:
    a. 80 sd 100
    b. 75 sd 120
    c. 110 sd 130
    d. 65 sd 85

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  • #5487
    R-Stats
    Keymaster

    Gunakan Tabel Z Distribusi Normal atau dengan menggunakan Excel untuk menyelesaikannya. Rumus penghitungannya menggunakan
    \[\begin{aligned} P(x_1 < X < x_2) &= P(X < x_2) - P(X < x_1)\\ &= P\left(Z < \frac{x_2 - \mu}{\sigma}\right) - P\left(Z < \frac{x_1 - \mu}{\sigma}\right) \end{aligned}\]

    1. \(P(80 < X < 100)\)
    2. \[\begin{aligned} P(80 < X < 100) &= P\left(Z < \frac{100 - 100}{20}\right) - P\left(Z < \frac{80 - 100}{20}\right)\\ &= P(Z < 0) - P(Z < -1)\\ &= 0\text{,}5 - 0\text{,}1587\\ &= 0\text{,}3413 \end{aligned}\]

    3. \(P(75 < X < 120)\)
    4. \[\begin{aligned} P(75 < X < 120) &= P\left(Z < \frac{120 - 100}{20}\right) - P\left(Z < \frac{75 - 100}{20}\right)\\ &= P(Z < 1) - P(Z < -1\text{,}25)\\ &= 0\text{,}8413 - 0\text{,}1056\\ &= 0\text{,}7357 \end{aligned}\]

    5. \(P(110 < X < 130)\)
    6. \[\begin{aligned} P(110 < X < 130) &= P\left(Z < \frac{130 - 100}{20}\right) - P\left(Z < \frac{110 - 100}{20}\right)\\ &= P(Z < 1\text{,}5) - P(Z < 0\text{,}5)\\ &= 0\text{,}9332 - 0\text{,}6915\\ &= 0\text{,}2417 \end{aligned}\]

    7. \(P(65 < X < 85)\)
    8. \[\begin{aligned} P(65 < X < 85) &= P\left(Z < \frac{85 - 100}{20}\right) - P\left(Z < \frac{65 - 100}{20}\right)\\ &= P(Z < -0\text{,}75) - P(Z < -1\text{,}75)\\ &= 0\text{,}2266 - 0\text{,}0401\\ &= 0\text{,}1866 \end{aligned}\]

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