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) = P( X < 248 when = 250) X - 250 248 - 250 < = P 5 / 25 5 / 25 = P(Z <-2)=0.002275 b) = P( X > 248 when = 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- / n z= 47.5 - 50 4 / 30 = -3.42 Reject H0 if z0 < - /2 where - 0.005 = - z z 2.58 or z0 > z/2 where z0.005 = 2.58 -3.42<-2.58 SO REJECT. b) For = 0.01, z/2 = z0.005 = 2.58 x - z 0.005 x + z 0.005 n n 4 4 47.5 - 2.58 47.5 + 2.58 30 30 45.616 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 /2 + z ) 2 2 2 = ( z 0.005 + z 0.10 ) 2 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 (n - n ) + k 2n 2 = k 2n 2 b) E(U)=2 2=k2n 2 k=1/2n ...
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This note was uploaded on 05/05/2008 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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