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# quiz1sol - IE-121-Spring 2003 Exam 1 1(30 points...

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Unformatted text preview: IE-121-Spring 2003 Exam 1 1.(30 points) F-T-T-F-T-T-T-F-T-F 2.(20 points) a) α = P( X < 248 when µ = 250) X − 250 248 − 250 < = P 5 / 25 5 / 25 = P(Z <-2)=0.002275 b) α = P( X > 248 when µ = 247) X − 247 248 − 247 > = P 5 / 25 5 / 25 = P(Z >1)=0.841345 =1-0.841345=0.158655 3.(20 points) a) z0 = x−µ σ/ n z= 47.5 − 50 4 / 30 = −3.42 Reject H0 if z0 < − α/2 where − 0.005 = − z z 2.58 or z0 > zα/2 where z0.005 = 2.58 -3.42<-2.58 SO REJECT. b) For α = 0.01, zα/2 = z0.005 = 2.58 σ σ x − z 0.005 ≤ µ ≤ x + z 0.005 n n 4 4 47.5 − 2.58 ≤ µ ≤ 47.5 + 2.58 30 30 45.616 ≤ µ ≤ 49.384 With 99% confidence, we believe the true mean yield of the chemical process is between 45.616% and 49.384%. c) n= (z α /2 + zβ ) σ 2 2 δ2 = ( z 0.005 + z 0.10 ) 2 σ 2 (48.5 − 50) 2 = (2.58 + 1.28) 2 (4) 2 = 105.9 = 106, (1.5) 2 4)(30 points) a) 2n 2n n n E (U ) = k[ E ∑ X i − ∑ X i + V ∑ X i − ∑ X i i = n +1 i = n +1 i =1 i =1 2 = k (nµ − nµ ) + k 2nσ 2 = k 2nσ 2 b) E(U)=σ2 σ2=k2n σ2 k=1/2n ...
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## This homework help was uploaded on 02/26/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .

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quiz1sol - IE-121-Spring 2003 Exam 1 1(30 points...

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