LIR 832 Qualifying Examination: Spring, 2004This examination consists of 10 equally weighted questions which require basicknowledge of statistics. The examination lasts two hours, additional time will not be provided. Z and T tables are attached at the end of the examination. Partial credit is given only forarithmetic errors. Your work must be organized so that the grader can readily determine wherethe error occurred to obtain partial credit1. We have taken a sample of our employees and calculated the time required to complete astandard task, the data from this study is provided in the following table. Calculate thesample mean and standard deviation of minutes to complete the task....Employee Minutes tocomplete task1921438465126112. A simple random sample of 20 students at a high school yields a sample mean(combined) SAT score of 960 with a sample standard deviation of 100. Conduct a 10%,5%, and 1% test of the alternative hypothesis that : … 1000.3. As part of a demographic study, you are interested in whether the mean number ofchildren for families in a given area is 2. In a simple random sample of 25 families, youfind the sample mean number of children is . Conduct the appropriate X=22.10%, 5% and 1% test of the alternative hypothesis that : > 2.0.4. Mary is a construction worker who is irregularly employed. Her wages per month have amean of $2,000 but a standard deviation of $1,000. Find that probability that her income in agiven month will exceed $1666.67 (assuming income is normally and independently distributedacross months)5. Asset income across individuals is normally distributed with an annual mean of $500 andannual standard deviation of $400. In a simple random sample of 30 individuals, what is theprobability that average asset income will exceed $600?6. A. You take a survey of your workforce and find that 55 percent of your employeeswant union representation. Suppose you selected two workers at random, withreplacement. What is the probability of selecting two workers who want unionrepresentation?B. At your plant, 16 percent of your employees have filed a grievance at some timein their tenure with your company. Similarly, 7 percent of your workforce hasfiled a grievance and won the case in arbitration. What is the probability that anemployee has won in grievance arbitration given that they have filed at least oneclaim?7. In a simple random sample of 36 families in a certain county, you find the sample meanincome is $9,500 and the sample standard deviation is $2,500. Using a 10%, 5% and 1%test, can you reject the null hypothesis that : $$9,000.8. A random variable Z has a standard normal distribution. What is the probability thatA. Z > 1.75B. Z < 1.10C. -1.2 < Z < 1.2D. .9 < Z < 2.19. We have been studying the frequency of absences in our firm. After collecting data onthe pattern of absences for our employees from several plants, we are able to construct aprobability distribution for absences.Days Absent Probability of Employee Being Absent XDays in the Last Year1 0.53 0.14 0.26 0.17 0.1Calculate the mean and standard deviation of absences for this firm.10. Assume that 10 percent of the population is left handed. Suppose you chose five peopleat random, what is the probability that two of them will be left handed. To help you withthis problem, the binomial formula is Pxnrnrpprnr()!(!)( )!**( )=−−−1Where:n is the size of the sampler is the number of successesp is the probability of a