mont4e_sm_ch05_sec05

# W nw w2 e n0 e2 we nw w2e2 wsp weights

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Unformatted text preview: 3.29 = 0.9612 5-64 X~N(160, 900) a) Let Y = X1 + X2 + ... + X25, E(Y) = 25E(X) = 4000, V(Y) = 252(900) = 22500 P(Y &gt; 4300) = ⎛ 4300 − 4000 ⎞ P⎜ Z &gt; ⎟ = P( Z &gt; 2) = 1 − P( Z &lt; 2) = 1 − 0.9773 = 0.0227 ⎜ ⎟ 22500 ⎠ ⎝ 5-38 ⎛ b) c) P( Y &gt; x) = 0.0001 implies that P⎜ Z &gt; ⎜ ⎝ Then x − 4000 150 x − 4000 ⎞ ⎟ = 0.0001. ⎟ 22500 ⎠ = 3.72 and x = 4558 5-65 W: weights of parts E: measurement error. W~ N(µw, σw2) , E ~ N(0, σe2) ,W+E ~ N(µw, σw2+σe2) . Wsp = weights of the specification P (a) P(W &gt; µw + 3σw) + P(W &lt; µw – 3σw) = P(Z &gt; 3) + P(Z &lt; -3) = 0.0027 (b) P(W+E &gt; µw + 3σw) + P( W+E &lt; µw – 3σw) = P (Z &gt; 3σw / (σw2+σe2)1/2) + P (Z &lt; -3σw / (σw2+σe2)1/2) Because σe2 = 0.5σw2 the probabili...
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## This document was uploaded on 02/09/2014.

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