11 - Probability Distributions Solutions 1 In each part...

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Probability Distributions - Solutions 1 In each part, indicate, (1) whether the variable is discrete or continuous AND (2) whether it is binomial or not AND (3) if it is binomial, give values for n and p . a. Number of times a “head” is flipped in 10 flips of a coin 1. Discrete 2. Binomial 3. n = 10, p = 0.5 b. Time to complete a 30 question multiple choice test 1. Continuous 2. Not Binomial since continuous c. Number of correct answers on a 30 question multiple choice test for somebody who randomly guesses at every question. There are four answer choices for each question, 1. Discrete 2. Binomial – counting correct answers 3. n = 30, p = 0.25 d. A woman buys a lottery ticket every week for which the probability of winning anything at all is 1/10. She continues to buy them until she has won 3 times. X = the number of tickets she buys. 1. Discrete 2. Not binomial since the number of trials is not fixed 2 In Stat 200 last year, students were asked to rate how much they liked various kinds of music on a scale of 1 (don’t like at all) to 6 (like very much). Following is a probability distribution (with one probability not given) for females’ rating of Top 40 music. X=Rating 1 2 3 4 5 6 Probability .04 .05 .09 ?? .32 .26 a. Is X = music rating a discrete variable or a continuous variable? Explain. Discrete. There are a small number of distinct possible outcomes (the ratings 1-6). b. What must be the value of the probability for X = 4 (the probability that rating equals 4)? Explain how you determined this. P(x=4) is 0.24 since all the probabilities need to add to 1. c. Determine E(X), the mean rating given by females. {HINT: Find (rating*probability) for each rating, and then add up those values.} E(X) = (1)(.04) + 2(.05) + 3(.09) + 4(.24) + 5(.32) + 6(.26) = .04+.10+.27+.96+1.60+1.56 = 4.53

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11 - Probability Distributions Solutions 1 In each part...

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