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Chapter 7

# Chapter 7 - Chapter 7 Random Variables Use the following to...

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Chapter 7: Random Variables Use the following to answer questions 1-2: A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had the following probability distribution: Value of X 1 2 3 4 Probability 0.2 0.4 0.3 0.1 1. Referring to the information above, the probability that a randomly chosen subject completes at least three puzzles in the five-minute period while listening to soothing music is A) 0.3. B) 0.4. C) 0.6. D) 0.9. Ans: B Section: 7.1 Discrete and Continuous Random Variables 2. Referring to the information above, P ( X < 3) has value Use the following to answer questions 3-5: Let the random variable X be a random number with the uniform density curve given below. 3. Referring to the information above, P ( X = 0.25) is Page 98

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Chapter 7: Random Variables 4. Referring to the information above, P ( X 0) has value 5. Referring to the information above, P (0.7 < X < 1.1) has value A) 0.30. B) 0.40. C) 0.60. D) 0.70. Ans: A Section: 7.1 Discrete and Continuous Random Variables 6. Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 4. You select two balls at random and without replacement from the box and note the two numbers observed. The sample space S consists of the three equally likely outcomes {(1, 2), (1, 3), (2, 3)}. X , the total of the two balls selected, has probabilities X 3 4 5 Probability 1/3 1/3 1/3 The probability that X is at least 4 is Use the following to answer questions 7-9: The probability density of a random variable X is given in the figure below. 7. Referring to the information above, from this density, the probability that X is between 0.5 and 1.5 is 8. Referring to the information above, the probability that X is at least 1.5 is Page 99
Chapter 7: Random Variables

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Chapter 7 - Chapter 7 Random Variables Use the following to...

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