機率問題(常態隨機變數)

2011-06-11 10:25 am

A Wall Street analyst estimates that the annual return from the stock of Company A can be considered to be an observation from a normal distribution with mean u=8.0% and standard deviation σ=1.5%. The analyst’s investment choices are based upon the consideration that any return greater than 5% is “satisfactory” and a return greater than 10% is “excellent”. What is the probability that Company A’s stock will prove to be “unsatisfactory”? The probability that Company A’s stock will prove to be “excellent” ?

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回答 (1)

[匿名]

2011-06-11 5:23 pm

✔ 最佳答案

X~N(8%,1,5%^2)，Z=（X-8%）/1.5%~N(0,1)依題意What is the probability that Company A’s stock will prove to be “unsatisfactory”?即求P（X≤5%）The probability that Company A’s stock will prove to be “excellent” ? 即求P（X>10%）P(X≤5%）=P(Z≤(5%-8%)/1.5%)=P(Z≤-2)=1-0.9772=0.0228P(X>10%)=1-P(X≤10%)=1-P（Z≤（10%-8%）/1.5%）=1-P(Z≤1.33)=1-0.8485=0.1515

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