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匿名
匿名 發問於 科學及數學數學 · 5 年前

Probability Question

Find k such that P(|Z| ≤ k) = 0.97 where Z follows the standard normal distribution.

3 個解答

評分
  • 5 年前
    最愛解答

    Find k such that P(|Z|<=k)=0.97 where Z follows the standard normal distribution

    Sol

    P(|Z|<=k)=0.97

    P(-k<=Z<=k)=0.97

    P(k)-P(-k)=0.97

    P(k)-[1-P(k)]=0.97

    2P(k)-1=0.97

    2P(k)=1.97

    P(k)=0.985

    k=2.17

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  • 5 年前

    Yin 網友,應該不對。

    考慮

    P(|Z| ≤ k) = P(-k ≤ Z ≤ k) = 0.97

    P(0 ≤ Z ≤ k) = 0.97/2 = 0.485

    再查表。

    2014-11-20 23:35:52 補充:

    Yin 網友,應該不對。

    考慮

    P(|Z| ≤ k) = P(-k ≤ Z ≤ k) = 0.97

    P(0 ≤ Z ≤ k) = 0.97/2 = 0.485

    再查表。

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  • 5 年前

    P(|Z| ≤ k) = 0.97

    P(0≤Z ≤ k)+P(-k≤Z ≤ 0) = 0.97

    by symmetry

    P(-k≤Z ≤ 0) = 0.485

    1 - P(Z≤-k) = 0.485

    P(Z≤-k) = 0.515

    k = -0.04

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