Statistics > EXAM > FINAL EXAM FOR STATS 100Amidterm1pspring14-ALL ANWERS CORRECT (All)

FINAL EXAM FOR STATS 100Amidterm1pspring14-ALL ANWERS CORRECT

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MULTIPLE CHOICE QUESTIONS. ONLY ONE ANSWER IS CORRECT. CHOICE MUST BE MARKED ON THE SCANTRON, AND ALSO HERE ON THE EXAM. ONLY THE SCANTRON WILL BE GRADED. NO MARKS ON SCANTRON OR MORE THAN ONE MARK WILL RESULT IN 0 POINTS FOR THE QUESTION NOT MARKED, EVEN IF IT IS MARKED ON THE EXAM. You may use the space near the question for scratch work, but scratch work will not be read. Question 1. Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% a blood test, and 22% both tests. What is the probability that a randomly selected DWI suspect is given a blood test or a breath test, but not both? (a) 0.7 (b) 0.3 (c) 0.08 (d) 0.22 (e) 0.12 Solution 1. P(Bbc [ Bcb) = (0:78 − 0:22) + (0:36 − 0:22) = 0:56 + 0:14 = 0:7 Question 2. Let S = (0; 1] and define Ai = ((1=i); 1]; i = 1; 2; :::::. The union of these events is (a) S, the whole sample space. (b) The interval [0; 0:5]. (c) The set with only 1 in it. (d) The empty set. (e) The interval [0; 10]. Solution 2. The union is the sample space, S1 i=1 Ai = (0; 1] = S Question 3. The Center for Disease Control says that about 30% of high school students smoke tobacco (down from a high of 38% in 1997). Suppose you randomly select high school students to survey them on their attitude towards scenes of smoking in the movies. What is the probability that the first smoker is the 6th person you choose? (a) 0.000729 (b) 0.0504 (c) 0.000504 (d) 0.5 (e) 0.002 April 19, 2014 3Stat 100A -Intro Probability Practice Midterm 1 J. Sanchez UCLA Department of Statistics Question 4. A series of 3 jobs arrive at a computing centre with 3 processors. Assume that each of the jobs is equally likely to go through any of the processors. Find the probability that all processors are occupied. Circle one, work will not be read. (a) 5/9 (b) 1/3 (c) 4/7 (d) 1/10 (e) 2/9 Solution 3. 2/9 Why? For all 3 processors to be busy when 3 jobs arrive, there must be one job in each processor. Thus the probability is (3!)=33 = 2=9 Question 5. Of 25 laptops available in a business, 10 are used by the accounting personnel (A), 5 are used by the management (M), and 15 are not used by anybody(N). Which of the following statements is true? (a) The number of laptops used by management or accounting but not used by both is 5 (b) The event MAc [ AMc has 10 laptops in it. (c) MAc contains 5 laptops. (d) The number of laptops used by at least one of the groups is 5. (e) MA is the empty set. Solution 4. Event Write event symbolically Number of laptops Used by management and accounting MA=M 5 Only used by management MAc Empty set, none Used by management or accounting but not used by both MAc [ AMc = MAc 5 Used by at least one of the groups M [ A 10 Question 6. A certain firm produces resistors and markets them as 10-ohm resistors. However, the actual ohms of resistance produced by the resistors may vary. Research has established that 10 percent of the values are below 8 ohms and 20 percent are above 10 ohms. If three resistors, randomly selected, are used in a system, what is the probability that the three resistors have values larger than

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