mont4e_sm_ch05_sec05

Xn404 y time of wheel firing yn609 xy n100 13 pxy

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Unformatted text preview: lt; 2.12) = 1 − 0.983 = 0.0170 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)/130.5) =P(Z<1.387) =0.917 (b) P(X+Y>110) = 1- P(Z<(110-100)/ 130.5) =1-P(Z<2.774) = 1-0.9972 =0.0028 5-59 a) X∼N(0.1, 0.00031) and Y∼N(0.23, 0.00017) Let T denote the total thickness. Then, T = X + Y and E(T) = 0.33 mm, V(T) = 0.000312 + 0.00017 2 = 1.25 x10 −7 mm 2 , and σ T = 0.000354 mm. 0.2337 − 0.33 ⎞ ⎛ P (T < 0.2337 ) = P ⎜ Z < ⎟ = P (Z < −272) ≅ 0 0.000354 ⎠ ⎝ b) P ( T > 0 . 2405 5-60 0 . 2405 − 0 . 33 ⎞ ⎛ ) = P⎜Z > ⎟ = P ( Z > − 253 ) = 1 − P ( Z < 253 ) ≅ 1 0 . 000345 ⎠ ⎝ Let D denote the width of the casing minus the width of the door. Then, D is normally distribut...
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