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Unformatted text preview: to detect an attack would become catastrophic. 3. #25 on page 92 Let r. v. X be the stock price X ∼ N (30, 8.2 2 ) a. At X = 40, 40 30 1.22 8.2 z − = = P (X ≤ 40) = P ( z ≤ 1.22) =.50 + .3888 = .8888 P (X ≥ 40) = P ( z ≥ 1.22) = 1 P (X ≤ 40) = 1  .8888 = .1112 b. At X = 20, 20 30 1.22 8.2 z − = = − P ( x ≤ 20) = P ( z ≤1.22) = P ( z ≥ 1.22) = 0.1112 c. Suppose let x be the stock price. P (Z ≥ z) = 0.1 ⇒ P (0 ≤ Z ≤ z) = 0.4 ⇒ z = 1.28 A zvalue of 1.28 cuts off an area of approximately 10% in the upper tail. x = 30 + 8.2(1.28) = 40.50 A stock price of $40.50 or higher will put a company in the top 10%. 4. #33 on page 93 a. 2 minutes (1/ μ =0.5 ? μ =2) b. let X be the time between telephone calls. P (X ≤ 30 seconds) = P (X ≤ 0.5 minutes) = 1  e0.5/2 = 0.221 c. P (X ≤ 1) = 1  e1/2 = 0.393 d. P ( x ≥ 5) = 1 P (X ≤ 5) = 1 (1  e5/2) = 10.918 = 0.082...
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 Spring '11
 Standard Deviation, 0.999..., Dr. Zhang, monthly order quantity

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