asked in 科學數學 · 1 decade ago

有關機率學的數學題目

A company establishes a fund of 120 from which it wants to pay an amount, C, to any of its 20 employees who achieve a high performance level during the coming year. Each employee has a 2% chance of achieving a high performance level during the coming year, independent of any other employee.

Determine the maximum value of C for which the probability is less than 1% that the fund will be inadequate to cover all payments for high performance.

請問這題的意思是在說什麼?該如何計算?

Update:

binomial distribution

1 Answer

Rating
  • Peta
    Lv 4
    1 decade ago
    Favorite Answer

    題目:

    一家公司設立了總金額 120 的基金,而 20 名的員工中只要年度表現優於某一水準,

    就可以獲得中的 C。每個員工成功贏得此獎金的機率為 2%,且與他人獲得的機率互相獨立。

    決定提供獎金 C 的最大值,使得總基金不足以支付所有獲獎員工的機率小於 1%。

    假設獲得此獎金的員工人數為 K,則此 K 為獨立隨機變數。

    恰好有 k 名員工獲得獎金的機率為:(binomial distriubion)

    Pr(K=k) = C(20,k)(0.02)^k (0.98)^(20-k), 其中 C(20,k) 表示 20 取 k 之所有取法的總數。

    總共需要支付的獎金金額為 kC,kC 大於 120 的機率小於 1%:

    Pr(kC>=120) < 0.01 或

    Pr(0<=k<120/C) >= 0.99

    查表

    http://wps.prenhall.com/wps/media/objects/4108/420...

    可知 120/C >= 2

    C <= 60,C 最大值為 60。

    2008-08-07 11:35:38 補充:

    http://en.wikipedia.org/wiki/Binomial_distribution

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