2008hw3_solutions

2008hw3_solutions - ST 314 HW #3 Solutions 1. Text, p. 133,...

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Unformatted text preview: ST 314 HW #3 Solutions 1. Text, p. 133, exercise 3.40. The r.v. Y is distributed exponential with = 0.01. a. P(Y < 30) = 1 e - (30) = 1 e-.01(30) = 1- e -.30 = .2592 b. P(Y > 15) = 1 [1 e - (15) ] = e-.15 = .8607 c. P(Y = 100) = 0 d. P(50 Y 150) = [1 e - (150) ] [1 e - (50) ] = -e-1.5 + e-.5 = .3834 2. Text, p. 141, exercise 3.47. Let Y = thickness of bolts. Then Y is normally distributed with mean = 10.0 mm and standard deviation = 1.6 mm. a. P(9.2 Y 10.8) = P( (9.2-10)/1.6 (Y- )/ (10.8-10)/1.6 ) = P (-.5 Z .5) = P(Z < .5) P(Z < -.5) = .6915 .3085 = .3830 b. P(Y 9.2) = P ((Y- )/ (9.2-10)/1.6) = P(Z -.5) = .3085 3. Text, p. 142, exercise 3.53. Let Y = volume percent. Then Y is normally distributed with = 70 and = 2. a. P(Y > 75) = P((Y- )/ > (75-70)/2) = P(Z > 2.5) = 1 - .9938 = .0062 b. P(67 < Y < 73) = P((67-70)/2 < Z < (73-70)/2) = P(-1.5 < Z < 1.5) = P(Z < 1.5) P(67 < Y < 73) = P((67-70)/2 < Z < (73-70)/2) = P(-1....
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This note was uploaded on 05/27/2008 for the course ST 314 taught by Professor Arthur during the Spring '08 term at Oregon State.

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2008hw3_solutions - ST 314 HW #3 Solutions 1. Text, p. 133,...

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