HW_Week3.docx - UMUC STAT-200 Homework Assignments Dr Brian...

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UMUC STAT-200 Homework Assignments Week #3 Dr. Brian Killough Textbook #1: Lane et al . Introduction to Statistics, David M. Lane et al., 2013. ( ) Textbook #2: Illowsky et al . Introductory Statistics, Barbara Illowsky et al., 2013. ( ) Lane - Chapter 5: 7,25,27 7. You flip a coin three times. (a) What is the probability of getting heads on only one of your flips? (1/2)(1/4)= 1/8 of a probability (b) What is the probability of getting heads on at least one flip? No heads = (1/2)(1/2)(1/2)= 1/8…. So 1- (1/8) = a probability of 7/8 25. You are to participate in an exam for which you had no chance to study, and for that reason cannot do anything but guess for each question (all questions being of the multiple choice type, so the chance of guessing the correct answer for each question is 1/d, d being the number of options (distractors) per question; so in case of a 4-choice question, your guess chance is ¼ = 0.25. Your instructor offers you the opportunity to choose amongst the following exam formats: Answers computed using the binomial probabilities formula: I. 6 questions of the 4-choice type; you pass when 5 or more answers are correct; .0044 probability II. 5 questions of the 5-choice type; you pass when 4 or more answers are correct; .01024 probability III. 4 questions of the 10-choice type; you pass when 3 or more answers are correct. .0036 probability Rank the three exam formats according to their attractiveness. It should be clear that the format with the highest probability to pass is the most attractive format. Which would you choose and why? HINT: Use the Binomial Probability function Most attractive = 5-choice type Middle attractive = 4-choice type Least attractive = 10-choice type I would choose the most attractive exam, because I have the highest probability of passing without having had studied.
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