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ADM 2303 STATISTICS FOR MANAGEMENT I FINAL EXAMINATION FALL 1990 DECEMBER 19, 1990 19:00 NAME (BLOCK LETTERS): STUDENT NUMBER: SIGNATURE: SECTION (circle one -- we may lose your mark if you have the wrong section): A: (Nash Wed 1300, Fri 1130) B: (Nash Wed 1000, Fri 0830) C: (Lane) D: (Kuttner) General instructions: Calculators, rulers and one (1) page of notes (8.5" by 11" or A4 size) allowed. All answers may REQUIRE a brief explanation of your work except where otherwise stated. To aid marking, some questions have a box for the answer, with space for working and comments. PLEASE ENSURE THE PRINCIPAL PART OF YOUR ANSWER IS IN THE BOX. Question Mark 1 6 2 5 3 13 4 14 5 7 6 8 7 12 8 10 9 12 10 13 1. Consider the following MINITAB Stem-and-Leaf display of the measured concentration of mercury in drinking water in parts per million (ppm) found for different municipalities in Northern Ontario and Quebec. MTB > stem c1 Stem-and-leaf of C1 N = 22 Leaf Unit = 0.10 4 0 0027 6 1 26 9 2 344 10 3 1 (4) 4 1117 8 5 7 7 6 88 5 7 1 4 8 16 2 9 39
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a. (2 marks) What are the lowest and highest mercury concentrations measured? b. (2 marks) What is the median mercury concentration? c. (2 marks) What is the lower quartile of mercury concentration? 2. Let X be a continuous Uniform random variable on the interval [1,3]; that is X can take on values between 1 and 3. a. (2 marks) What is the probability density function of X? b. Find and explain briefly: (i) (1 marks) P(X=2) (ii) ( 2 marks) P(2<X<5) 3. A panel of candidates to be interviewed consists of 5 women and 4 men. 3 candidates are chosen at random from the panel. a. (i) (2 marks) Since the sampling is done without replacement, what is the probability of choosing 2 women? (ii) (5 marks) Let X be a random variable representing the number of WOMEN drawn in the sample of 3 (without replacement). Write out the probability function of X. b. Regardless of your result in part (a)., assume the probability of drawing no MEN is 0.1, of drawing 1 MAN is .5, of drawing 2 MEN is .3, and of drawing 3 MEN is .1. (i) (3 marks) What is the expected value of the number of WOMEN drawn? (ii) (3 marks) What is the standard deviation of the number of WOMEN drawn? 4. Let X represent the return (in $) on investment for a share in Fred's Fast Food Franchise and Y be the return (in $) on investment for a share in Sal's Slimming Salons. Assume X and Y are continuous, random variables. The following is some information about their expected values: E(X) = 5 E(X^2) = 30 E(Y) = 4 Var(Y) = 12 COV(X, Y) = - 6 a. (1 mark) Attach appropriate units to the quantities above. b. Find the following, making sure you explain your work or the answer: (i) (2 marks) Var X (ii) (2 marks) E(XY) (iii) (2 marks) The expected return on a portfolio of 100 shares of Fred's and 200 shares of Sal's. (iv) (2 marks) The standard deviation of the return on the portfolio
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