Name ECON 307Economics 307: Principles and Methods of StatisticsAssignment 3

Due Date: March 1, 2013

Directions: Please hand in a hard copy of the solutions for this assignment. Only the solution toquestion five must be typed up and properly formated. For questions 1 through 4 please circle your answer.Because I post answer keys to Blackboard after the due date has passed, in fairness to all students, lateassignments will incur a score penalty.

1. It is known that amounts of money spent on clothing in a year by students on a particular campusfollow a normal distribution with a mean of $380 and a standard deviation of $50.

(a) What is the probability that a randomly chosen student will spend less than $400 on clothing ina year?

(b) What is the probability that a randomly chosen student will spend more than $360 on clothingin a year?

(c) Draw a graph to illustrate why the answers to parts (a) and (b) are the same.

(d) What is the probability that a randomly chosen student will spend between $300 and $400 onclothing in a year?

(e) Compute a range of yearly clothing expenditures - measured in dollars - that includes 80% of allstudents on this campus. Explain why any number of ranges could be found, and find the shortestone.

Name ECON 307

2. A machine operation produces bearings with diameters that are normally distributed with mean 3.0005inches and standard deviation 0.0010 inch. Specifications require that bearing diameters lie in theinterval 3.0000 ± 0.0020 inches. Those outside the interval are considered scrap and must be re-machined.

(a) With the existing machine setting, what fraction of total production will be scrap?

(b) Suppose that five bearings are randomly drawn from production. What is the probability that atleast one is defective?

(c) What should the mean diameter be in order that the fraction of bearings scrapped be minimized?

3. Scores on an examination are assumed to be normally distributed with mean 78 and variance 36.

(a) What is the probability that a person taking the examination scores higher than 72?

(b) Suppose that students scoring in the top 10% of this distribution are to receive an A grade. Whatis the minimum score a student must achieve to earn an A grade.

(c) What must be the cutoff point for passing the examination if the examiner wants only the top28.1% of all scores to be passing?

(d) Approximately what proportion of students have scores 5 or more points above the score thatcuts off the lowest 25%?

(e) If it is known that a student’s score exceeds 72, what is the probability that his or her scoreexceeds 84?

4. The SAT and ACT college entrance exams are taken by thousands of students each year. The math-ematics portion of each of these exams produces scores that are approximately normally distributed.In recent years, SAT mathematics exam scores have averaged 480 with standard deviation 100. Theaverage and standard deviation for ACT mathematics scores are 18 and 7, respectively. An engineer-ing school sets 550 as the minimum SAT math score for new students. What percentage of studentswill score below 550 in a typical year? What score should the engineering school set as a comparablestandard on the ACT math test?

Name ECON 307

5. Imagine that you are a policy analyst for a Department of government of your choice. The Departmentis interested in the microeconomic behavior of individuals in the area of your choosing. With thatscenario as a backdrop, please visit the U.S. Department of Labor, Bureau of Labor Statistics, NationalLongitudinal Survey of Youth and your knowledge of data description to respond to the followingquestions. Select three variables for your analysis. Choose one qualitative and two quantitative variable.The 1979 cohort provides for a greater number of variables and observations while the 1997 cohortprovides for interesting information as well. Both are excellent sources of data.

Data: http://www.bls.gov/nls/

For health expenditure data a good alternative source of data, should you so decide, is the MedicalExpenditure Panel Survey. http://meps.ahrq.gov/mepsweb/data stats/MEPSnetHC.jsp

(a) In a brief paragraph, describe why you chose these variables. What makes them important orrelevant for your Department to consider?

(b) Discuss how people tend to perform on these measures and across the groups you have selected.Answer this question by using the mean, standard deviation and range and creating a well for-mated histogram for one of the variables of your choice. Does the distribution appear normal? Inyour answer create (a) a clear table of results (don’t just paste in the excel file) and (b) a well-developed paragraph of accompanying discussion. The table and paragraph should be developedso that they are technically complete, but so that policy makers can incorporate this informationinto the formation of policies, that is, for an audience of people who have no statistical training.

(c) Separate the data into two groups based on the qualitative variable. How do the two groupscompare along the quantitative variables? Answer this question by using the mean, median andthe standard deviation and range. In your answer create (a) a clear table of results (don’t justpaste in the excel file) and (b) a well-developed paragraph of accompanying discussion. The tableand paragraph should be developed so that they are technically complete, but directed at audienceof people who have no statistical training.