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Mind on Statistics Test Bank Chapter 8 Mind on Statistics Chapter 8 Sections 8.1 - 8.2 Questions 1 to 4: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. 1. Random variable X = the number of letters in a word picked at random out of the dictionary. A. Discrete random variable B. Continuous random variable KEY: A 2. Random variable X = the number of letters in the last name of a student picked at random from a class on English composition. A. Discrete random variable B. Continuous random variable KEY: A 3. Random variable X = the time (in seconds) it takes one email to travel between a sender and receiver. A. Discrete random variable B. Continuous random variable KEY: B 4. Random variable X = the weight (in pounds) a dieter will lose after following a two week weight loss program. A. Discrete random variable B. Continuous random variable KEY: B 5. Which one of these variables is a continuous random variable? A. The time it takes a randomly selected student to complete an exam. B. The number of tattoos a randomly selected person has. C. The number of women taller than 68 inches in a random sample of 5 women. D. The number of correct guesses on a multiple choice test. KEY: A 6. Which one of these ‘X’ variables is a discrete random variable? A. An experiment in chemistry is repeated many times and X is the time required for a reaction to occur in seconds. B. A student is randomly selected and X is the number of correct answers on a two question multiple-choice quiz. C. A UPS package is randomly selected and X is the weight in pounds of the package. D. A student is randomly selected and X is the distance they must travel in feet to go from their dorm room door to the door of their first class on Monday morning. KEY: B 143 Chapter 8 Questions 7 to 10: The probability distribution for X = number of heads in 4 tosses of a fair coin is partially given in the table below. k 0 1 2 3 4 P(X = k) 1/16 4/16 6/16 4/16 ? 7. What is the probability of getting 4 heads? A. 1/16 B. 2/16 C. 4/16 D. Cannot be determined KEY: A 8. What is the probability of getting at least one head? A. 1/16 B. 4/16 C. 5/16 D. 15/16 KEY: D 9. What is the probability of getting 1 or 2 heads? A. 4/16 B. 6/16 C. 10/16 D. 14/16 KEY: C 10. What is the value of the cumulative distribution function at 3, i.e. P(X ≤ 3)? A. 6/16 B. 10/16 C. 11/16 D. 15/16 KEY: D 144 Chapter 8 Questions 11 to 13: Based on her past experience, a professor knows that the probability distribution for X = number of students who come to her office hours on Wednesday is given below. k 0 1 2 3 4 P(X = k) 0.10 0.20 0.50 0.15 0.05 11. What is the probability that at least 2 students come to office hours on Wednesday? A. 0.50 B. 0.70 C. 0.80 D. 0.90 KEY: B 12. What is the value of the cumulative probability distribution at 2, i.e. P(X ≤ 2)? A. 0.50 B. 0.70 C. 0.80 D. 0.90 KEY: C 13. What is the probability that at least 1 student comes to office hours on Wednesday? A. 0.50 B. 0.70 C. 0.80 D. 0.90 KEY: D 145 Chapter 8 Questions 14 to 17: In an experiment, a person guesses which one of three different cards a researcher has randomly picked (and hidden from the person who guesses). This is repeated four times, replacing the cards each time. Let X = number of correct guesses in the four tries. The probability distribution for X, assuming the person is just guessing, is partially provided below. No. of Correct Guesses, X 0 1 2 3 4 Probability 0.20 0.39 0.30 0.10 14. What is the value of the missing probability P(X = 4)? KEY: 0.01 15. What is the probability that the person would get 3 or more correct guesses? KEY: 0.11 16. What is the value of P(X 2) = probability that number of correct guesses is less than or equal to 2? KEY: 0.89 17. Give the cumulative distribution function for the number of correct guesses. KEY: See table below. No. of Correct Guesses, X 0 1 2 3 4 Cumulative Probability 0.20 0.59 0.89 0.99 1.00 Questions 18 and 19: Ellen is taking 4 courses for the semester. She believes that the probability distribution function for X = the number of courses for which she will get an A grade is given below. No. of A’s, X 0 1 2 3 4 Probability 0.10 0.30 0.40 0.15 0.05 18. What is the probability that Ellen will get at least 2 A’s? KEY: 0.60 19. What is the value of the cumulative probability distribution at 3, i.e. P(X ≤ 3)? KEY: 0.95 146 Chapter 8 Section 8.3 Questions 20 to 22: Joan has noticed that the probability distribution for X = number of students in line to use the campus ATM machine when she shows up to use it is shown below. k 0 1 2 3 4 P(X = k) 0.10 0.10 0.40 0.30 0.10 20. What is the probability that there will be no more than 1 student in line when Joan shows up? A. 0.10 B. 0.20 C. 0.70 D. 0.90 KEY: B 21. What is the expected value of X, E(X)? A. 2.0 B. 2.2 C. 2.5 D. 3.0 KEY: B 22. The variance of X, V(X) = 1.16. What is the standard deviation of X? A. 1.08 B. 1.16 C. 1.35 D. 2.20 KEY: A 23. The payoff (X) for a lottery game has the following probability distribution. Payoff, X $0 $5 Probability 0.8 0.2 What is the expected payoff? A. $0 B. $0.50 C. $1.00 D. $2.50 KEY: C 24. The expected value of a random variable is the A. value that has the highest probability of occurring. B. mean value over an infinite number of observations of the variable. C. largest value that will ever occur. D. most common value over an infinite number of observations of the variable. KEY: B 25. In a gambling game, on every play, there is a 0.1 probability that you win $7 and a 0.9 probability that you lose $1. What is the expected value of this game? A. +$2 B. $0.20 C. $2 D. $0.20 KEY: D 147 Chapter 8 26. Suppose that for X = net amount won or lost in a lottery game, the expected value is E(X) = $0.50. What is the correct interpretation of this value? A. The most likely outcome of a single play is a net loss of 50 cents. B. A player will have a net loss of 50 cents every single time he or she plays this lottery game. C. Over a large number of plays the average outcome for plays is a net loss of 50 cents. D. A mistake must have been made because it’s impossible for an expected value to be negative KEY: C 27. The formula for the standard deviation for any discrete random variables with values xi and corresponding probabilities pi is: A. xi pi 2 B. (xi ) pi 2 C. (xi ) pi KEY: B 28. What characteristic of a random variable is described by the expected value? A. Standard deviation B. Mean C. Most likely value D. Maximum value KEY: B 29. The following probability distribution is for the random variable X = number of classes for which full time students at a university are enrolled in a semester: No. of classes, X 4 5 6 7 Probability 0.2 0.5 0.2 0.1 What is the mean number (expected value) of courses taken per student? A. 4 B. 5 C. 5.2 D. 5.5 KEY: C 30. The expected value for a random variable is A. the long-run average. B. the most likely value. C. the most frequent value observed in a random sample of observations of the random variable. D. always np. KEY: A 31. The mean for a population of N values is equivalent to A. the mean of any random sample taken from the population. B. the median of the population of N values. C. the expected value of a random variable defined as X = value for a randomly sampled individual from the population. D. Np where p = proportion of values in the population that are unique. KEY: C 148 Chapter 8 Questions 32 to 34: Ellen is taking 4 courses for the semester. She believes that the probability distribution function for X = the number of courses for which she will get an A grade is given below. No. of A’s, X 0 1 2 3 4 Probability 0.10 0.30 0.40 0.15 0.05 32. What is the expected number of A’s she will get? (i.e.
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