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匿名 發問於 科學及數學數學 · 9 年 前

Normal Distribution

For X ~ N(2,4), find the value of x if P(x < X < 3.1) = 0.62.

更新:

To: 螞蟻雄兵. Please explain how to get P[(x -2)/2 < (X - 2)/2 < 0.55] = 0.7088 - P[(x -2)/2]

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  • 9 年 前
    最佳解答

    Normal Distribution

    For X ~ N(2,4),find the value of x if P(x < X< 3.1) = 0.62

    Sol

    P(x < X < 3.1)

    =P[(x-2)/2<(X-2)/2 <(3.1-2)/2]

    =P[(x-2)/2<(X-2)/2 <0.55]

    =0.7088-p[(x-2)/2]

    =0.62

    P[(x-2)/2]=0.0888

    1-0.0888=0.9112

    P(1.34)=0.9099,P(1.35)=0.9115

    (0.9115-0.9099)/(1.35-1.34)=(0.9115-0.9112)/(1.35-y)

    0.0016/0.01=0.0003/(1.35-y)

    1.35-y=0.01*0.0003/0.0016=0.001875

    y=1.348125

    (x-2)/2=-1.348125

    x-2=-2.69625

    x=-0.69625

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