Hwk3SolnGdDrtBSp09 - Solution to Homework III Spring...

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Solution to Homework III Spring Semester 2009 Question 1. Let X = Number of minutes per day a customer views cable television. We have X ~ N(75, 20) A) P(X>80) = . 4013 . ) 25 . ( ) 20 75 80 ( ) 80 ( = = - = - - Z P Z P X P σ μ (From Z- table) B) P(X<60) = = - < = - < = - < - ) 75 . ( ) 20 75 60 ( ) 60 ( Z P Z P X P 2266 . )] 75 . ( = + Z P . C) ) 20 75 85 20 75 65 ( ) 85 65 ( ) 85 65 ( - < < - = - < - < - = < < Z P X P X P =P(-.5 < Z < .5) = 1- 2P(Z > .5) = 1- 2(.3085) = .3830 D) C) ) 20 75 70 20 75 55 ( ) 70 55 ( ) 70 55 ( - < < - = - < - < - = < < Z P X P X P = P(-1 < Z < -.25) = P(+.25 < Z < +1) = P(Z > .25) – P(Z >1) = .4013 - .1587 = .2426. Ei) Y ~ B(50, .2266) = B(n, π). Here we must assume that the number of minutes viewed between rooms is independent. This is pretty reasonable, since the viewing habits of those in different rooms shouldn’t influence each other. However, they could be correlated because of the weather. If the weather is lousy and everyone’s staying in for the night, then viewing across rooms may all go up. Similarly, if the weather is beautiful, everyone may go out, so viewing for everyone would go down. So it is possible viewing times between rooms would be correlated. But it is reasonable to assume that these measures would be, in general, independent. ii) P(Y = 8) = . 0767 . ) 2266 . 1 ( ) 2266 (. ! 8 ! 42 ! 50 42 8 = - Binomial with n = 50 and p = 0.2266 x P( X = x ) 8 0.0767239 iii) P(Y < 8) = .170. Binomial with n = 50 and p = 0.2266 x P( X <= x ) 8 0.170016 iv) P(Y > 12) = 1 – P(Y < 11) = 1 - .535 = .465.
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Homework III Solution Spring 2009 Binomial with n = 50 and p = 0.2266 x P( X <= x ) 11 0.535201 Question 2 P Probability Diagram Table Value Minitab A P(t 10 > 3.15) .005< A < 0.01 A = 0.005166 B P(t 10 < -4.09) .001 < B < 0.005 B = 0.001090 C P(t 10 < -2.18 or t 10 > 2.18) .05 < C < 0.1 C = 0.05425 D P(t 10 > 1.98) .025 < D < 0.05 D = 0.037936 E P(t 10 < -2.51) .01 < E < 0.025 E = 0.015456 F P(t 10 > 1.12)
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This note was uploaded on 10/09/2009 for the course H ADM 201 at Cornell University (Engineering School).

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Hwk3SolnGdDrtBSp09 - Solution to Homework III Spring...

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