Chapter 7 Review Questions

Chapter 7 Review Questions Answer the following multiple choice questions: 1. Suppose X is a random variable with mean µ. Suppose we observe X many times and keep track of the average of the observed values. The law of large numbers says that (a) The value of µ will get larger and larger as we observe X. (b) As we observe X more and more, this average and the value of µ will get larger and larger. (c) This average will get closer and closer to µ as we observe X more and more often. (d) As we observe X more and more, this average will get to be a larger and larger multiple of µ. (e) None of the above 2. In a population of students, the number of calculators owned is a random variable X with P(X = 0) = 0.2, P(X = 1) = 0.6, and P(X = 2) = 0.2. The mean of this probability distribution is (a) 0 (b) 2 (c) 1 (d) 0.5 (e) The answer cannot be computed from the information given. 3. Refer to the previous problem. The variance of this probability distribution is (a) 1 (b) 0.63 (c) 0.5 (d) 0.4 (e) The answer cannot be computed from the information given. 4. The number of calories in a one-ounce serving of a certain breakfast cereal is a random variable with mean 110. The number of calories in a full cup of whole milk is a random variable with mean 140. For breakfast you eat one ounce of the cereal with 1/2 cup of whole milk. Let Z be the random variable that represents the total number of calories in this breakfast. The mean of Z is (a) 110 (b) 140 (c) 180 (d) 250 (e) 195 5. The weight of reports produced in a certain department has a normal distribution with mean 60g and standard deviation 12g. What is the probability that the next report will weigh less than 45g? (a) 0.1042 (b) 0.1056 (c) 0.3944 (d) 0.0418 (e) The answer cannot be computed from the information given. 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. X had the following distribution: X 1 2 3 4 P(X) .2 .4 .3 .1 6. Using the above data, what is the probability that a randomly chosen subject completes at least 3 puzzles in the five-minute period while listening to soothing music? (a) 0.3 (b) 0.4 (c) 0.6 (d) 0.9 (e) The answer cannot be computed from the information given. 7. Using the above data, P(X < 3) is (a) 0.3 (b) 0.4 (c) 0.6 (d) 0.9 (e) The answer cannot be computed from the information given. 8. If X and Y are independent random variables with standard deviations of 3 and 4, respectively, find the standard deviation of the sum of X and Y. (a) 2.5 (b) 3.5 (c) 5.0 (d) 7.0 (e) The answer cannot be computed from the information given. 9. Which of the following random variables should be considered continuous? (a) The time it takes for a randomly chosen woman to run 100 meters (b) The number of brothers a randomly chosen person has (c) The number of cars owned by a randomly chosen adult male (d) The number of orders received by a mail order company in a randomly chosen week (e) None of the above 10. Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is normal with mean $360 and standard deviation $50. What is the value of P(X > $400)? (a) 0.2119 (b) 0.2881 (c) 0.7881 (d) 0.8450 (e) The answer cannot be computed from the information given. Answers: 1. c 5. b 9. a 2. c 6. b 10. a 3. d 7. c 4. c 8. c