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Unformatted text preview: YhcConne...l \ MAT 221 Final Exam May 7,2007 NAME  SECTION _ Instructions: Work all 8 problems on the test paper. You may turn in additional pages if needed, but make sure your name is on each page. You may use your calculators, but be sure to explain what calculations were done by the calculator so you can receive partial credit for the method ifthe final answer turns out to be wrong. All necessary tables are attached, so a calculator should only be needed to do arithmetic. No books, notes, or collaboration with others. PLEASE SILENCE CELL PHONES DURING THE TEST. (Please do not write below. The spaces below are for grading purposes.) 1. 6. 2. 7. 3. 8. 4. Total 5. Problem 1. (15 points) The times (in minutes) it took 15 runners to complete a race were: 110, 132, 126, 153, 164, 141, 122, 130, 144, 158, 148, 147, 149, 153, 161 a. Create a stem plot of these data. b. Find the fivenumber summary. c. List any outliers. Justify your answer using the 1.5 x IQR rule. If there are no outliers, say none. Problem 2. (10 points) The following data show how many hours students slept the night before an exam and their score on the exam. I Hours slept (x) I 8 7 I 7 I 8 I 6 I 5 I 7 4 I 9 I 3 60 I 89 I 69 I Test score (y) I 83 86 I 74 I 88 I 76 I 63 I 90 a. Make a scatter plot of these data. b. Compute the correlation coefficient for these two variables. (To ease the computations, you may use that the standard deviation of the test scores is 11.0739 and that the sum of all the products xy is equal to 5137.) c. What conclusion (if any) is suggested by the value ofthis correlation coefficient? Problem 3. (10 points) Given that A and B are independent events with peA) = 0.7 and PCB) = 0.4, find: a) peA and B), b) P(BIA), and, c) peA or B) Problem 4 (15 points) Suppose a bag contains four coins 3 real coins and 1 fake coin. The real coins have a head and a tail. The fake coin has two heads. A coin is selected at random and flipped. a) Draw a tree diagram to represent the coin selected and the result ofthe flip. Label the branches with the appropriate probabilities. b) What is the probability that you get a head on the flip? c) Given that the flip is a head, what is the probability that you selected the fake coin? Problem 5. (10 points) The heights of American women are normally distributed with mean 65.5 inches and standard deviation 2.5 inches. a. What is the probability that a randomly chosen American woman's height is greater than 66.7 inches? b. What is the minimum height of an American woman in the top 10% of the population? Problem 6 (10 points) A teacher, who is measuring the IQ's of high school students, collects a random sample of 10 scores with a sample mean of 108.2. Assume that the standard deviation (0) for the population of all high school students' IQ's is 14....
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