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LIR 832 midterm Spring 2004 answer key

# LIR 832 midterm Spring 2004 answer key - LIR 832 Mid-term...

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LIR 832: Mid-term Examination: Spring, 2004 Each Problem is worth 20 points. Answer five of the six problems. Problems should be answered as thoroughly as you are able. Partial credit on problems is only possible if I can locate errors in your calculations; neatness and organization of your answers is essential Remember, answer only five of the six problems, if you chose to answer all, I will select the five with the lowest scores. 1. A random variable X is normally distributed. What is the probability of observing a value of X such that: a. X > 220 where X has a mean of 200 and a variance of 144 P(X>220) = P[Z>(220-200)/12] = P(Z>20/12) = P(Z>1.667) = .0475 = 4.75% b. X < -25 where X has a mean of -10 and a variance of 121 P(X<-25) = P[Z<(-25-(-10))/11] = P(Z<(-15/11)) = P(Z<(-1.36)) = .0869 = 8.69% c. 1510 < X < 1535 where X has a mean of 1520 and a variance of 49 P(1510 < X < 1535) = P[(1510-1520)/7 < Z < (1535-1520)/7] = P[-10/7 < Z < 15/7] = P(-1.43 < Z < 2.14) = 1 – (.0764+.0162) = 1 – (.0926) = .9074 = 90.74% d. X > 2000 or X < -1000 where X has a mean of 500 and a variance of 225 P(X>2000) + P(X<-1000) = P[Z>(2000-500)/15] + P[Z<(-1000-500)/15] = P(Z>1500/15) + P(Z<-1500/15) = P(Z>100) + P(Z<-100) = Approximately zero. e. .0012 > X > .0009 where X has a mean of .001 and a variance of .000196 P(.0012 > X > .0009) = P[(.0012-.001)/.014 > Z > (.0009-.001)/.014] = P[(.0002/.014) > Z > (-.0001/.014)] = P(.014 > Z > 0) + P(.007>Z>0) = (.5 - .4960) + (.5-.4960) = .008%. To get this you could round 0.014 to 0.01 and 0.007 to 0.01. If you had access to http://www-stat.stanford.edu/~naras/jsm/FindProbability.html you could find the precise probability = 0.837%

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2. A consultant is peddling a program which she promises will increase the productivity of our employees. The premise of the program is that when communication between plant management and employees is not good employees feel little attachment or loyalty to the firm. The program aims to improve communication by increasing the contact between plant management, clericals and production employees through structured informal interactions: management walk arounds, meetings between employees and managers and even some dinners in which plant managers host small groups of employees. An acquaintance of yours has tried this program at six of her plants (these were chosen by random sampling from her thirty plants. All plants are identical and should produce the same dollar value per employee). Three of the plants were controls, no change was made in managerial/employee interaction; three of the plants implemented this program. We have data on the percentage of employees who met with plant management for at least an hour over the last month and the dollar value of output in the following month Percent Meeting Management Value of Output per Employee plant 1 10 100 plant 2 15 95 plant 3 13 107 plant 4 55 105 plant 5 65 93 plant 6 85 115 Percent meeting management is the percent of employees who met management in the prior month. Value of output per employee is the dollar value of output in

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LIR 832 midterm Spring 2004 answer key - LIR 832 Mid-term...

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