You are to take a multiple-choice exam consisting of 64 questions with two possible responses to each question. Suppose that you have not studied and so must guess (select one of the two answers in a...

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Extracted text: You are to take a multiple-choice exam consisting of 64 questions with two possible responses to each question. Suppose that you have not studied and so must guess (select one of the two answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test. In USE SALT (a) What kind of probability distribution does x have? binomial geometric (b) What is your expected score on the exam? (Hint: Your expected score is the mean value of the x distribution.) 32 (c) Calculate the variance of x. 16 Calculate the standard deviation of x. 4 (d) Based on your answers to parts (b) and (c), is it likely that you would score over 50 on this exam? Explain the reasoning behind your answer. A score of 50 is standard deviations from the mean in the distribution of x. So a score of over 50 is ver v ---Select--- likely unlikely