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midterm1-solutions

# midterm1-solutions - Statistics 5021 Midterm 1 Name...

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Statistics 5021 Midterm 1 Name: Internet-ID: There are 4 questions, with point values given in parentheses for each part of each question. Show all work to receive credit. You are allowed one 8.5x11 inch sheet of paper with your notes written on both sides. You are permitted to use a calculator. Question Points Earned Points Possible 1 3 2 4 3 4 4 9 Total 20 1

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1. The experiment is to roll a 6-sided die. (a) (1 point) Write down the sample space S , that is, list all possible outcomes of this experiment. Solution: S = { 1 , 2 , 3 , 4 , 5 , 6 } (b) (1 point) Let A be the event that the die shows a value of at least 5. Write down the outcomes in A . Also write down the outcomes in A c . Solution: A = { 5 , 6 } A c = { 1 , 2 , 3 , 4 } (c) (1 point) Compute P ( A c A ). Solution: Since there are zero outcomes in the event A c A , that is, A c A = , P ( A c A ) = P ( ) = 0. Notice that we did not need to assume anything about the probabilities of the outcomes in S since we are computing the probability of an event with zero outcomes. 2. Suppose that 1% of batteries produced by a factory are truly defective. The factory tests each battery it produces. This test has the following performance: Among batteries that are truly defective, 98% were labeled defective by the test.
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midterm1-solutions - Statistics 5021 Midterm 1 Name...

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