data analysis ch 5 study guide
12. If there are 13 heart cards in a deck of 52 cards, then what is the probability of selecting one heart card on a single draw from the deck of cards? A) 13/52 B) 1/52 C) 26/52 D) 1/13
A) 13/52
29. Which of the following is a mathematical formula that relates the conditional and marginal (unconditional) probabilities of two conditional outcomes that occur at random? A) Bayes' theorem B) simple probability C) random event sampling D) descriptive statistics
A) Bayes' theorem
20. The probability that someone in the human population has blood type AB is about p = .08; the probability that someone has blood type O is about p = .25. Knowing that each individual can have one and only one blood type, what is the probability that a person has an AB or O blood type? A) .33 B) .02 C) 1.00 D) This state of affairs is not possible.
A) .33
38. Below is the probability distribution for the number of times students had to take the same exam before passing it. If a student must pass the exam in two tries of less to pass the class, then what is the probability of passing the class? x-------1-------2-------3-------4 p(x)---0.4-----0.4-----0.1------0.1 A) .80 B) .40 C) .20 D) .10
A) .80
11. A gambler rolls a 3 with one roll of a single fair die. Given that the die was six-sided, what was the probability of rolling a 3 with one roll? A) 1/6 B) 3/6 C) 1/9 D) 3/9
A) 1/6
37. Below is the probability distribution for random variable x. Which of the following is most probable? x-------12-------13-------14 p(x)----0.55----0.35----0.10 A) a score of at most 13 B) a score of at least 13 C) a score of 12 D) a score of 14
A) a score of at most 13
18. Which rule states that when two outcomes are mutually exclusive, the probability that either one of these outcomes will occur is the sum of their individual probabilities? A) additive rule B) multiplicative rule C) both A and B D) none of the above
A) additive rule
47. A distribution of probabilities for random outcomes of a bivariate or dichotomous random variable is called a A) binomial probability distribution B) distribution of expected values C) random variable distribution D) mathematical expectation
A) binomial probability distribution
41. A researcher records the number of buckets of popcorn purchased by patrons during one night at the movies. She finds that the probability that a patron purchased 0 buckets of popcorn is p = .27; 1 bucket is p = .51; 2 buckets is p = .17; and 3 buckets is p = .05. How many buckets of popcorn can we expect a patron to purchase per night at the movies in the long run? A) exactly 1 bucket of popcorn per night B) more than 1 bucket of popcorn per night C) less than one bucket of popcorn per night D) none of the above
A) exactly 1 bucket of popcorn per night
27. The probability of a team having a sellout crowd is p = .45. The probability of having a sellout crowd and the team winning is p = .32. Hence, the probability of a team winning, GIVEN that they have a sellout crowd, is A) p = .71 B) p = .77 C) p = .14 D) There is not enough information to answer this question.
A) p = .71
1. The proportion or fraction of times an outcome is likely to occur is referred to as A) probability B) a random event C) sample space D) luck
A) probability
13. Probability allows us to make predictions regarding: A) random events B) random outcomes C) random variables D) all of the above
A) random events
15. Two outcomes are said to be mutually exclusive when A) the probability of the two outcomes occurring together is equal to zero (p = 0) B) the probability of the occurrence of one outcome has no effect on the probability of the occurrence of the second outcome C) the probability of the two outcomes occurring together is greater than zero (p > 0) D) the probability of the two outcomes occurring together sums to one
A) the probability of the two outcomes occurring together is equal to zero (p = 0)
***40. Suppose you open a new game at the county fair. When patrons win, you pay them $3.00; when patrons lose, they pay you $1.00. If the probability of a patron winning is p = .20, then how much can you expect to win (or lose) in the long run? Hint: You need to compute the expected value of the mean. A) win 0.20 cents per play B) win 0.60 cents per play C) lose 0.80 cents per play D) lose 2.20 dollars per play
A) win 0.20 cents per play
10. A researcher finds that 20 of 120 students failed an exam. In this case, the probability of failing this exam was A) .14 B) .17 C) .20 D) unknown
B) .17
3. A therapist goes through her records and finds that 200 of her 400 patients showed significant improvement in mental health over the past year. Hence, the probability of her patients showing significant improvement in mental health is A) .05 B) .50 C) 200 D) 400
B) .50
44. Below is the probability distribution for random variable x. What is the standard deviation of this probability distribution? x------1-------2-------3 p(x)---0.24---0.52---0.24 A) 0.48 B) 0.69 C) 0.24 D) 2.00
B) 0.69
4. A news poll showed that voters had no preference for either of three candidates. In this example, the probability of a vote for, say, Candidate A equals A) 1/2 B) 1/3 C) 2/3 D) 1.00
B) 1/3
32. Which of the following probability distributions is accurate? A) 45/80, 20/80, 20/80, 10/80 B) 10/80, 23/80, 37/80, 10/80 C) ñ20/80, 40/80, 40/80, 20/80 D) none of the above
B) 10/80, 23/80, 37/80, 10/80
45. Below is the probability distribution for random variable x. What is the standard deviation of this probability distribution? x--------0--------4--------8 p(x)-----0.85----0.05-----0.10 A) 6.20 B) 2.49 C) 1.00 D) 0.35
B) 2.49
14. The following are six random outcomes for a sample space: -1, -3, -3, -2, -5, and -6. What is the probability of selecting a -3 in this example? A) 1/6 B) 2/6 C) -2/6 D) -3/6
B) 2/6
50. A researcher reports that the probability of a college student living on campus is p = .38. If a small local college has 2,000 students enrolled, then what is the standard deviation of college students living on campus? Hint: This is a binomial probability distribution. A) 471.2 students B) 21.7 students C) 760 students D) There is not enough information to answer this question.
B) 21.7 students
49. A researcher determines that the probability of missing class among students at a local school is p = .16. Assuming that the school has 300 students enrolled, how many students can we expect to miss class on a given day? Hint: This is a binomial probability distribution. A) 252 students B) 48 students C) 16 students D) There is not enough information to answer this question.
B) 48 students
24. When the sum of the probabilities of two outcomes is exhaustive of all possible outcomes, these outcomes are referred to as A) mutually exclusive B) complementary C) independent D) conditional
B) complementary
39. The mean of a probability distribution is called the A) expected value of the mean B) mathematical expectation C) both A and B D) none of the above
B) mathematical expectation
21. Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities? A) additive rule B) multiplicative rule C) both A and B D) none the of above
B) multiplicative rule
26. The probability of a college student being employed is p = .35. The probability of a student being employed and dropping out of college is p = .20. Hence, the probability of a student dropping out of college, GIVEN that he or she is employed, is A) p = .07 B) p = .57 C) p = .55 D) There is not enough information to answer this question.
B) p = .57
31. The distribution of probabilities for each outcome of a random variable that sums to 1.00 is called a A) random variable B) probability distribution C) conditional probability D) sample space
B) probability distribution
34. A researcher records the number of job openings among small businesses. She finds that the probability that a small business has 0 job openings is p = .22; 1 job opening is p = .45; 2 job openings is p = .08; and 3 job openings is p = .25. What is the probability that a small business has at least 2 job openings? A) .08 B) .25 C) .33 D) .67
C) .33
5. A researcher has participants choose between three advertisements. She finds that 54 prefer Ad A, 86 prefer Ad B, and 60 prefer Ad C. The probability or proportion of participants preferring Ad B is A) .86 B) .60 C) .43 D) 86
C) .43
19. In a game, the probability of winning money is p = .16, the probability of losing money is p = .54, and the probability of breaking even is p = .30. What is the probability of winning or losing money in this game? A) .16 B) .54 C) .70 D) 1.00
C) .70
17. A researcher determines the probability that a research study will reveal something new is p = .80. What is the probability that the study will reveal something new or not reveal something new? A) .80 B) .64 C) 1.00 D) .16
C) 1.00
43. If the standard deviation of a probability distribution is 9, then the variance is A) 3 B) 9 C) 81 D) unknown
C) 81
33. A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate? A) Yes, it distributes all possible outcomes for the random variable. B) No, one of the outcomes is stated as "or more." C) No, the probability distribution does not sum to 1.0. D) both B and C
C) No, the probability distribution does not sum to 1.0.
30. Bayes' theorem is often applied to a variety of ________ probability situations, including those related to statistical inference. A) generic B) absolute C) conditional D) fixed
C) conditional
28. The probability of a student attending every college class is p = .26. The probability of a student attending every college class and earning an A is p = .22. Hence, the probability of a student earning an A, GIVEN that he or she attends every college class, is A) p = .06 B) p = .48 C) p = .85 D) There is not enough information to answer this question.
C) p = .85
8. The total number of possible outcomes for a random variable is referred to as A) probability B) a random event C) the sample space D) the sum
C) the sample space
23. The probability that a parent rewards a child with a dessert for eating a healthy meal is .07. Assuming independent outcomes, the probability that two parents reward their child's healthy eating equals A) .07 B) .14 C) .05 D) .005
D) .005
22. Suppose that the probability that any child of alcoholic parents becomes alcoholic is p = .16. Assuming independent outcomes, the probability that two children of alcoholic parents will be alcoholic equals A) .16 B) .32 C) .25 D) .03
D) .03
9. A researcher records the following data for the number of bids made on a sample of items sold at an auction. Based on the table, what was the probability that an item had 7 bids made on it? number of bids-----Frequencies 3---------------------5 4---------------------12 5---------------------7 6---------------------6 7---------------------10 A) 5 B) 10 C) .10 D) .25
D) .25
35. A professor records the grades for his class of students. He finds that the probability that a student earns an A is p = .14; earns a B is p = .36; earns a C is p = .32; earns a D is p = .10; and earns an F is p = .08. What is the probability that a student earns a B or better in this class? A) .36 B) .14 C) .86 D) .50
D) .50
36. Below is the probability distribution for random variable x. What is the probability of at least a score of 2 in this distribution? x------1------2------3 p(x)--0.18---0.42---0.40 A) .18 B) .42 C) .60 D) .82
D) .82
42. If the variance of a probability distribution is 121, then the standard deviation is A) 121 B) 21 C) 12 D) 11
D) 11
46. Below is the probability distribution for the number of times students had to take the same exam before passing it. What is the value at the second standard deviation above the mean for this probability distribution? x--------1--------2--------3--------4 p(x)----0.40----0.40----0.10------0.10 A) 3.10 B) 3.40 C) 3.90 D) 3.78
D) 3.78
7. Which of the following is NOT a characteristic of probability? A) Probability varies between 0 and 1. B) Probability can never be negative. C) Probability can be stated as a fraction or decimal. D) Probability is most useful for describing fixed events.
D) Probability is most useful for describing fixed events.
16. A researcher determines that the probability of winning a new game is p = .32. Assuming winning and losing are mutually exclusive events, what is the probability of winning and losing the new game? A) .22 B) .68 C) 1.00 D) This outcome is not possible.
D) This outcome is not possible.
2. By definition, the probability of an outcome or event is A) the proportion of times an outcome is likely to occur B) the fraction of times an outcome is likely to occur C) particularly useful for predicting the likelihood of random events D) all of the above
D) all of the above
25. When the probability of one outcome changes depending on the occurrence of a second outcome, these outcomes are referred to as A) mutually exclusive B) complementary C) independent D) conditional
D) conditional
48. Each of the following is an example of a binomial distribution, except A) the number of heads in ten flips of a fair coin B) the number of males and females in a sample C) the number of votes for or against a candidate D) the time it takes to complete a driving test
D) the time it takes to complete a driving test
6. A researcher visits a population of 1,200 local residents to determine the proportion of local residents who support a new smoking ban. In this case, the sample space is A) equal to the number of residents who support the new smoking ban B) equal to the total number (or population) of residents C) equal to more than just these 1,200 residents D) unknown
D) unknown
