LIR 832 SPRING 2007 Problem Set 1

LIR 832 SPRING 2007 Problem Set 1 - LIR 832: Problem Set #1...

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LIR 832: Problem Set #1 Calculating Means, Variances and Standard Deviations: 1. Absenteeism in our plant varies considerably from day to day. Over the last ten days the number of employees absent has been 10, 15, 5, 6, 7, 22, 3, 14, 8, 21 a. Calculate the mean, variance and standard deviation of absences. The plant has 80 employees. Repeat these calculations for the percent of employees absent. b. Calculate the median and mode for this data set for the values. How do the median, mode and mean compare? 2. The midterm test for a statistics course has a time limit of 1 hour. However, like most statistics exams, this one was quite easy. To assess how easy, the professor recorded the amount of time taken by a sample of nine students to hand in their test papers. The times, rounded to the nearest minute, are 33 29 45 60 42 19 52 38 36 a. compute the mean, median and mode. What can you learn about the exam from these three statistics? 3. A plant which is under our supervision is in the midst of an organizing drive by Local 9 of the United Clerical Employees. There are ten employees in the clerical unit at this plant. Prior subtle and illegal research suggests that 45% of our clerical employees at all of our locations, sympathic to union representation. Using the binomial distribution, what is the likelihood that six or more of the employees in this ten employee unit will vote for a union? To calculate this outcome, you will need to use the binomial formula and calculate the likelihood of six, seven, eight, nine or ten employees will vote for a union (and then add these probabilities). Before trying to use the formula you will need to establish: a. What is the probability of a success (a vote for the union)? b. What is the probability of a failure (a vote against the union)? c. What is the total number of experiments? d. What is the number of successes (this will vary with the outcome you are calculating). Remember, n! is n*(n-1)*(n-2)*(n-3)*. ....5*4*3*2*1 and 0! = 1 so, for example, 6! = 6*5*4*3*2*1.
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4. We are developing a business plan for a psychic hot line. Based on our work with other similar services and the type of advertising we intend to do, we expect that the line will average 14 calls per hour. We also know that people who use these hot lines hate to wait to get answers to life’s most troubling questions. Calculate that probability that we will get at least 14 15, . .... 24 calls per hour.
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LIR 832 SPRING 2007 Problem Set 1 - LIR 832: Problem Set #1...

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