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

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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) = - < - 25 / 5 250 248 25 / 5 250 X P = P(Z <-2)=0.002275 b) α = P( X > 248 when μ = 247) = - - 25 / 5 247 248 25 / 5 247 X P = P(Z >1)=0.841345 =1-0.841345=0.158655 3.(20 points) a) z x n 0 = - μ σ / 42 . 3 30 / 4 50 5 . 47 - = - = z Reject H 0 if z 0 < - z α /2 where - z 0.005 = - 2.58 or z 0 > z α /2 where z 0.005 = 2.58 -3.42<-2.58 SO REJECT. b) For α = 0.01, z α /2 = z 0.005 = 2.58 + - n z x n z x σ μ σ 005 . 0 005 . 0 + - 30 4 58 . 2 5 . 47 30 4 58 . 2 5 . 47 μ 45.616 μ 49.384 With 99% confidence, we believe the true mean yield of the chemical process
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