Missing data from the first exercise of the second assignment 1 Concordia University Department of Economics ECON 221/2 - Sections A, B, and BB Instructors: B. Campbell, G. Tsoublekas Fall 2015 - ASSIGNMENT 2 Due in Class on Tuesday, October 27, 2015 Name: I.D. Section: 1. A manufacturer of network computer server systems is interested in improving the customer support service. As a first step, its marketing department has been charged with the responsibility of summarizing the extent of customer problems in terms of system downtime. The 40 most recent customers were surveyed to determine the amount of downtime in hours they had experienced in the previous month. The survey data are shown below. [The calculations and the graph for this exercise must be done on Excel. With the data on class intervals and frequencies that are shown below, you will create a table on Excel with the necessary detailed column calculations that will be used as a basis to answer sub-questions (a), (b), (d) and (e). You will paste your table here.] (24 points) a) Construct a cumulative frequency distribution, and a cumulative relative frequency distribution. (4 points) b) Using Excel, draw a histogram of the frequencies and paste it in the space provided below. (5 points) 2 c) On the basis of the shape of the histogram, make a rough assessment about symmetry in the data and the implication for the mean number of hours of downtime. (3 points) d) Using the appropriate formula for grouped data, calculate the mean number of hours in downtime. (Use the table provided above for your computations). (4 points) e) Using the appropriate formulas for grouped data, calculate the variance and the standard deviation. (Use the table provided above for your computations). (4 points) f) Calculate the Coefficient of Variation. (4 points) 3 2. The scores of all applicants taking an aptitude test required by a law school follow a normal distribution with mean 420 and standard deviation 100. (24 points) a.What is the probability that a randomly selected applicant will score less than 450 in this test? (4 points) b. What is the probability that two randomly (and independently) selected applicants will both score less than 450 in this test? (4 points) c. What is the probability that out of two randomly (and independently) selected applicants, at least one will score less than 450 in this test? (4 points) d. What is the probability that an applicant will score between 400 and 450? (4 points) 4 e. There is a 10% probability that an applicant will score above what number? (4 points) f. There is a 33% probability that the mean score of an applicant is less than what number? (4 points) 3. The ages of a random sample of people who attended a recent soccer match are as follows: (24 points) 23 12 37 18 35 35 40 20 17 38 14 27 29 23 22 37 13 49 27 20 38 18 40 29 15 15 19 65 31 17 45 23 53 42 21 a. Construct a stem-and-leaf display of the ages of those spectators. (4 points) 5 b. Find the median and the inter-quartile range. (5 points) c. Write down the five-number summary and draw a Box-and Whisker plot to show it. (5 points) 6 d. Group the data into 6 classes with their respective frequencies. Create a table on Excel with the necessary detailed column calculations to find the mean, variance, and the coefficient of variation. Paste your table here and show your formula calculations. (10 points) 4. The incomes of all families in a particular suburb can be represented by a continuous random variable. It is known that the median income for all families in this suburb is $60,000 and that 40% of all families in the suburb have incomes above $72,000. (8 points) a. For a randomly chosen family, what is the probability that its income will be between $60,000 and $72,000? (4 points) 7 b. Given no further information is available, what can be said about the probability that a randomly chosen family has an income below $65,000? (4 points) 5. A portfolio manager has asked you to analyze a newly acquired portfolio to determine its value and variability. The portfolio consists of 50 shares of Alpha Music and 40 shares of Beta Shows. Analysis of past history indicates that the share price of Alpha Music has a mean of $25 and variance of 121. Similarly, Beta Shows has a mean share price of $40 with a variance of 225. Your best evidence indicates that the share prices have a correlation coefficient of +0.5. (10 points) a. Compute the mean value and variance of the portfolio. (5 points) b. If the correlation coefficient between the share prices were actually - 0.5, what would be the mean value and the variance of the portfolio? (5 points) 8 6. EXCEL Problem: The objective is to Simulate a Bivariate Normal Distribution (n = 1000) at different levels of correlation RHO (). (10 points) a. Use the \"Random Number Generation\" function to create two columns of length 1000 that are independent N(0,1). Call the variables ZA and ZB. (2 points) b. Define a third variable: ZC = *ZA + (1-2)0.5*ZB The variables ZA and ZC are distributed bivariate normal with correlation . c. Using Excel defined functions fx, calculate the means and standard deviations of the three variables ZA, ZB, and ZC. (2 points) d. Create histograms for the 3 variables for = 0.5. Do the results surprise you? (2 points) 9 e. For = 0.7 calculate the value Pr[ZA < .0] and Pr [ZA < .0 & ZC < .0]. (2 points) f. Fill in the following table. (2 points) = -1.0 -0.7 -0.3 0.0 0.3 0.7 1.0 Do the results make sense to you? Pr [ZA < .0 & ZC < .0]