IE360%20HW4%20solutions

# IE360%20HW4%20solutions - IE 360 Homework Assignment#4...

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IE 360 Homework Assignment #4 Solutions 5-58 5-64 5-66 6-2 6-32 6-66 6-86 b & c only 5-58 (a) X: time of wheel throwing. X~N(40,4) Y : time of wheel firing. Y~N(60,9) X+Y ~ N(100, 13) P(X+Y 95) = P(Z<(95-100)/13 0.5 ) =P(Z<-1.387) =0.082264 (b) P(X+Y>110) = 1- P(Z<(110-100)/ 13 0.5 ) =1-P(Z<2.774) = 1-0.9972 =0.0028 5-64 X~N(160, 900) a) Let Y = X 1 + X 2 + . .. + X 25 E(Y) = E(X 1 )+ E(X 2 ) + . .. + E(X 25 ) = 25E(X) = 4000 V(Y) = V(X 1 )+ V(X 2 ) + . .. + V(X 25 ) = 25V(X) = 22500 P(Y > 4300) = 0227 . 0 9773 . 0 1 ) 2 ( 1 ) 2 ( 22500 4000 4300 = = < = > = > Z P Z P Z P b) P( Y > x ) = 0.0001 implies that . 0001 . 0 22500 4000 = > x Z P Then 150 4000 x = 3.72 and 4558 = x 5-66 D = A - B - C a) E(D) = 10 - 2 - 2 = 6 mm mm mm D V D 1225 . 0 015 . 0 05 . 0 05 . 0 1 . 0 ) ( 2 2 2 2 = = + + = σ b) P(D < 5.9) = P(Z < 1225 . 0 6 9 . 5 ) = P(Z < -0.82) = 0.206.

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6-2 Results for: EX06_02.MTW Descriptive Statistics: C1 Variable Mean StDev Variance Median

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IE360%20HW4%20solutions - IE 360 Homework Assignment#4...

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