STAT 170 exam 2
13. A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 6.
1/6
56. Fill in the blank to complete the statement. The mean age of all of a country's vice presidents when they took office would be a _____.
parameter
71. In a recent poll of 1200 randomly selected adult office workers, 32% said they had worn a Halloween costume to the office at least once. Report the 95% confidence interval for the proportion of all adult office workers who have worn a Halloween costume to the office at least once. Round final calculations to the nearest tenth of a percent.
(29.4%, 34.6%)
14. A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 10.
0
49. Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the question that follows, consider a sample of ten randomly selected people who recently booked an airline ticket. What is the probability that no more than three out of ten people used an online travel website when they book their airline ticket? Round to three decimal places.
0.007
38. A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 345 seconds.
0.0107
25. Suppose that a recent poll of American households about car ownership found that for households with a car, 39% owned a sedan, 33% owned a van, and 7% owned a sports car. Suppose that three households are selected randomly and with replacement. What is the probability that all three randomly selected households own a van?
0.036
52. The probability that a football game will go into overtime is 13%. What is the probability that two of three football games will go to into overtime? Round to three decimal places.
0.044
67. A pollotarian is a person who eats poultry but no red meat. A wedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is to be held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population of about 200,000. Suppose the wedding planner assumes that 5% of the guests will be pollotarian so she orders 15 pollotarian meals. What is the approximate probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals? Round to four decimal places.
0.079
72. From a random sample of workers at a large corporation you find that 58% of 200 went on a vacation last year away from home for at least a week. What is the margin of error for the 95% confidence interval of (0.50, 0.66) of coworkers who went on a vacation last year away from home for at least a week?
0.08
12. Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other. If one student is randomly chosen from the group, what is the probability that the student is male and chose "outside employment" as their most likely activity on a Saturday morning?
0.10
17. A random sample of car buyers was asked to respond to a survey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other. If one car buyer is randomly chosen from the group, what is the probability that the buyer is male and chose "manufacturer reputation" as their most important factor for the purchase?
0.100
18. A random sample of car buyers was asked to respond to a survey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other. If one car buyer is randomly chosen from the group, what is the probability that the buyer is female and chose "fuel efficiency" or "other" as their most important factor for the purchase?
0.110
69. A pescatarian is a person who eats fish and seafood but no other animal. An event planner does some research and finds that approximately 2.75% of the people in the area where a large event is to be held are pescatarian. Treat the 250 guests expected at the event as a simple random sample from the local population of about 150,000. Suppose the event planner assumes that 4% of the guests will be pescatarian so he orders 10 pescatarian meals. What is the approximate probability that more than 4% of the guests are pescatarian and that he will not have enough pescatarian meals? Round to three decimal places.
0.113
11. Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other. If one student is randomly chosen from the group, what is the probability that the student is female and chose "outside employment" as their most likely activity on a Saturday morning?
0.13
51. The probability that an individual has 20-20 vision is 0.13. In a class of 52 students, what is the probability of finding five people with 20-20 vision? Round to three decimal places.
0.139
16. A random sample of car buyers was asked to respond to a survey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other. If one car buyer is randomly chosen from the group, what is the probability that the buyer chose a car based on "looks" as their most important factor for the purchase?
0.160
48. Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the question that follows, consider a sample of ten randomly selected people who recently booked an airline ticket. What is the probability that at least nine out of ten people used an online travel website when they booked their airline ticket? Round to three decimal places.
0.183
26. Suppose that a recent poll of American households about car ownership found that for households with a car, 39% owned a sedan, 33% owned a van, and 7% owned a sports car. Suppose that three households are selected randomly and with replacement. What is the probability that at least one of the three randomly selected households own a sports car?
0.200
6. Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other. If one student is randomly chosen from the group, what is the probability that the student chose "outside employment" as their most likely activity on a Saturday morning?
0.23
36. Using the accompanying probability distribution curve, answer the question. What is the probability that the variable has a value greater than 6?
0.250
24. Suppose that a recent poll of American households about pet ownership found that for households with pets, 45% owned a dog, 34% owned a cat, and 10% owned a bird. Suppose that three households are selected randomly and with replacement and the ownership is mutually exclusive. What is the probability that none of the three randomly selected households own a cat?
0.29
19. A random sample of car buyers was asked to respond to a survey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other. If one car buyer is randomly chosen from the group, what is the probability amongst female buyers that they chose "price" as their most important factor for the purchase?
0.375
9. Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other. If one student is randomly chosen from the group, what is the probability that the student chose "recreation" or "other" as their most likely activity on a Saturday morning?
0.375
10. Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other. If one student is randomly chosen from the group, what is the probability that the student chose "homework" or "housework" as their most likely activity on a Saturday morning?
0.395
7. Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other. If one student is randomly chosen from the group, what is the probability that the student is male?
0.48
15. A random sample of car buyers was asked to respond to a survey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other. If one car buyer is randomly chosen from the group, what is the probability that the buyer is female?
0.52
20. A random sample of car buyers was asked to respond to a survey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other. Find the probability of those car buyers who chose "looks" as their most important factor was a female car buyer?
0.531
8. Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other. What is the probability that a randomly chosen survey respondent is male or chose "recreation" as their most likely activity on Saturday mornings?
0.675
23. If one of the 993 subjects is randomly selected, find the probability that the person chosen is a nonsmoker given that the person is a woman. Round to three decimal places.
0.684
40. The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 3.5 and 6 minutes to find a parking spot in the library lot.
0.7745
50. Five identical poker chips are tossed in a hat and mixed up. Two of the chips have been marked with an X to indicate that if drawn a valuable prize will be awarded. If you and two of your friends each draws a chip (with replacement), what is the probability that at least one of your group of three will win the valuable prize? Round to three decimal places.
0.784
39. A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 335 seconds to run the mile. Round to four decimal places.
0.9893
43. Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find the IQ score separating the top 14% from the others. Round to one decimal place.
116.2
62. According to a snack cracker manufacturer, a batch of butter crackers has a defect rate of 6%. Suppose a quality inspector randomly inspects 400 crackers. Complete the following statement. The quality inspector should expect _______ defective crackers, give or take ______ crackers.
24; 5
35. A box contains recipes from five categories. The following table shows the possible categories and the associated probability for a recipe randomly chosen. What is the probability of randomly selecting either an appetizer or salad category?
38.3%
53. Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket. Out of ten randomly selected people, how many would you expect to use an online travel website to book their hotel, give or take how many? Round to the nearest whole person.
7 people, give or take 1 person
41. The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the distribution of time is approximately normally distributed. For a randomly selected worker, what's the approximate probability the bolt will be inserted in 19 minutes or less? Round to the nearest whole percent.
84%
42. Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find the IQ score separating the bottom 30% from the top 70%. Round to one decimal place.
92.2
5. The National Center for Health Statistics has found that there is a 0.41% chance that an American citizen will die from falling. What is the probability that you will not die from a fall? Round to the nearest hundredth of a percent.
99.59%
1. If 20 babies are born, how often are there 8 or less male babies? Assume that the gender of a baby is a random event. Which of the following experiments would not simulate this situation?
A. Flip a coin twenty times. Designate a head to mean "female" and a tail to mean "male". B. Roll a die twenty times. Designate a 1, 2, or 3 to mean "female" and a 4, 5, or 6 to mean "male". C. Choose the first twenty digits from a row in the random number table. Designate odd numbers to mean "female" and even numbers to mean "male". D. All of these will simulate the gender of twenty babies.
61. Which of the following statements is not true about a sampling distribution?
A. It gives characteristics of the estimator, such as bias and precision. Your answer is not correct. B. It gives probabilities for a statistic. C.It is used for making inferences about a sample. This is the correct answer. D. It is the probability distribution of a statistic.
66. A medical study examined data on patients with cardiovascular disease who were currently non-smokers and those who were current smokers. Population 1 were smokers and population 2 were non-smokers. After data analysis, the 95% confidence interval for the difference in proportions is 0.015+/−0.011. Which of the following is the most accurate interpretation?
A. We are 95% confident that the difference in the proportion of smokers compared to nonsmokers is between 0.004 and 0.026. There is a significance difference indicating higher cardiovascular disease amongst smokers. This is the correct answer. B. We are 95% confident that the difference in the proportion of smokers compared to nonsmokers is between −0.004 and 0.026. There is not a significance difference in the proportions. C. We are 95% confident that the interval of the difference in the proportions contains zero. There is not a significance difference between smokers and non-smokers. Your answer is not correct. D. We are 95% confident that the proportion of smokers compared to non-smokers is between 0.004 and 0.026.
37. Suppose that weights of cans of Benneke brand peaches have a population mean of 13.5 ounces and a population standard deviation of 0.33 ounces and are approximately normally distributed. Which of the following statements are correct?
A. The probability that a randomly selected can of Benneke peaches will weigh between 12.9 ounces and 13.6 ounces is approximately 0.585. Your answer is not correct. B. Approximately 95% of all Benneke brand canned peaches will weigh between 12.85 ounces and 14.15 ounces. C. About 4% of all cans of Benneke peaches will weigh less than 12.9 ounces D. All of these statements are true.
22. A study asks a sample of adults whether they prefer cats or dogs or neither. Only one answer is allowed. Survey also records whether male or female. Which of the following are mutually exclusive events in this study?
Adult is male and likes cats and dogs.
78. Complete the statement by filling in the blanks. A larger sample size will improve the precision of the confidence interval, therefore, assuming no other values change, the margin of error will _____ and the confidence interval will be _____.
Decrease; narrower.
2. Is the following an example of theoretical probability or empirical probability? A homeowner notes that five out of seven days the newspaper arrives before 5 pm. He concludes that the probability that the newspaper will arrive before 5 pm tomorrow is about 71%.
Empirical
79. Which of the following statements is true about the confidence interval for a population proportion?
It is equal to the sample proportion plus or minus a calculated amount called the margin of error.
45. Decide whether the experiment is a binomial experiment. If it is not, explain why. You draw a marble 550 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn. After each draw, you place the marble back in the bag.
Not a binomial experiment. There are more than two outcomes.
47. Determine which of the given procedures describe a binomial distribution.
Observing that ten out of the next twenty customers at a grocery store checkout use a credit card given that the probability of using a credit card is 0.58.
21. Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other. Which of the following are mutually exclusive events?
Student chose "recreation" and student chose "other" as their most likely activity on Saturday mornings.
60. The government of a town needs to determine if the city's residents will support the construction of a new town hall. The government decides to conduct a survey of a sample of the city's residents. Which one of the following procedures would be most appropriate for obtaining a sample of the town's residents?
Survey a random sample of persons within each geographic region of the city.
31. Which of the following statements is true about the Law of Large Numbers (LLN)?
The LLN states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.
68. A polling agency wants to estimate the proportion of U.S. citizens who support the president's domestic policies. They surveyed 2500 U.S. citizens and found a 95% confidence interval for the difference in proportions between men and women who support the president's domestic policies as (−0.025 to 0.050) where population 1 is men and population 2 is women. Select the correct interpretation of this result.
The interval contains zero which shows that there is no significant difference in the proportions between men and women.
70. A polling agency wants to compare support for the president's foreign policies between men and women. They surveyed 2500 U.S. citizens and found a 95% confidence interval for the difference in proportions between men and women who support the president's foreign policies as (−0.05 to −0.025) where population 1 is men and population 2 is women. Select the correct interpretation of this result.
The interval estimates that p1−p2<0 which shows that women are more likely than men to support with the president's foreign policies.
46. Determine which of the given procedures describe a binomial distribution.
The number out of the next ten customers at a hotdog stand order who order onions, assuming that each has the same probability of ordering onions.
65. Suppose that Illinois lawmakers survey 130 randomly selected registered voters to see if they favor charging a deposit on aluminum cans to encourage recycling. The lawmakers believe the population proportion in favor of changing the law is 93% (based on historical data and previous votes). Which of the following conditions for the Central Limit theorem are not met?
The population proportion is too small and will not have enough expected failures.
63. Suppose that New Mexico lawmakers survey 160 randomly selected registered voters to see if they favor stricter laws regarding motorcycle helmet use for riders over the age of 17. The lawmakers believe the population proportion in favor of changing the law is 6% (based on historical data and previous votes). Which of the following conditions for the Central Limit theorem are not met?
The population proportion is too small and will not have enough expected successes.
73. Suppose that in a recent poll of 1200 adults between the ages of 35 and 45, 38% surveyed said they have thought about getting elective plastic surgery. Find the 95% confidence interval for the proportion of adults ages 35 to 45 who have thought about getting elective plastic surgery then choose the correct interpretation. Round to the nearest tenth of a percent.
The population proportion of adults ages 35 to 45 who have thought about getting elective plastic surgery is between 35.3% and 40.7%, with a confidence level of 95%.
44. Decide whether the experiment is a binomial experiment. If it is not, explain why. You observe the gender of the next 750 babies born at a local hospital. The random variable represents the number of boys.
binomial experiment
33. Determine whether the variable would best be modeled as continuous or discrete. The temperature of a cup of coffee dispensed from a beverage vending machine, taken four times during a 24-hour period.
continuous
54. Suppose that the probability that a person between the ages of 19 and 24 checks their daily horoscope is 0.12. If 400 randomly selected people between the ages of 19 and 24 were asked "Do you check your daily horoscope?", would you be surprised if 63 or more said yes to this question? Why?
Yes, 63 would be an unusually large number of people given the known probability of 0.12.
32. Answer the question about the Law of Large Numbers. A fair coin is tossed 3000 times. What can you say about getting the outcome of exactly 1500 tails?
You should not expect exactly 1500 tails in 3000 tosses, but the proportion of tails should approach 0.5 as the number of tosses increases.
27. Use your intuition to decide whether the following events are likely to be independent or associated. Event A: A randomly selected person is married with no children. Event B: A randomly selected person opposes a tax credit for children.
associated
28. Use your intuition to decide whether the following events are likely to be independent or associated. Event A: The randomly selected carton of milk you purchased from the store is sour. Event B: Your car won't start on a randomly selected morning.
independent
29. Classify the events as independent or not independent: Events A and B, where the probability of event A occurring is 0.2, the probability of event B occurring is 0.8, and the probability of both events occurring is 0.16.
independent
34. An MP3 playlist, containing several songs from five genres, is set to shuffle. The following table shows the genre and the associated probability for the first song played. Does the table represent a probability distribution?
no
30. Classify the events as independent or not independent: Events A and B, where the probability of event A occurring is 0.2, the probability of event B occurring is 0.5, and the probability of both events occurring is 0.09.
not independent
55. Fill in the blank to complete the statement. The collection of the ages of all of a country's first ladies when they married is a _____.
population
57. Fill in the blank to complete the statement. Researchers are interested in learning more about the age of men when they marry for the first time so they survey 500 married or divorced men and ask them how old they were when they first married. The mean of age of the 500 men when they married for the first time would be a _____.
statistic
58. A magazine publisher always mails out a questionnaire six months before a subscription ends. This questionnaire asks its subscribers if they are going to renew their subscriptions. On average, only 5% of the subscribers respond to the questionnaire. Of the 5% who do respond, an average of 49% say that they will renew their subscription. This 5% who respond to the questionnaire are known as what?
the sample
3. Is the following an example of theoretical probability or empirical probability? At a carnival shell game the player can pay three dollars and choose the shell that he or she believes is hiding the prize. There are four shells that are thoroughly mixed up after each guess. The player concludes that there is a one in four chance of randomly picking the winning shell.
theoretical
4. A bag contains 7 red marbles, 2 blue marbles, and 4 green marbles. Jeffery claims that if a marble is selected at random from the bag, the probability of choosing a blue marble is 2/13. Is this an example of empirical probability or theoretical probability?
theoretical
59. Max is interested in whether there is community interest in having local musicians perform music in the park in the evenings during the summer. Max goes to the park for several evenings in a row and asks people visiting the park whether they would like to hear music in the evening. Out of the 200 people he surveys, 58% respond favorably. This scenario is describing what type of sampling bias?
voluntary response bias
75. A researcher wishes to estimate the proportion of adults in the city of Darby who are vegetarian. In a random sample of 1255 adults from this city, the proportion that are vegetarian is 0.069. Find a 90% confidence interval for the proportion of all adults in the city of Darby that are vegetarians. Round to three decimal places.
(0.057, 0.081)
77. In a sample of 687 patients who underwent a certain type of surgery, 17% experienced complications. Find a 99% confidence interval for the proportion of all those undergoing this surgery who experience complications. Round to three decimal places.
(0.133, 0.207)
64. In a random sample of 37 Democrats from one city, 30 approved of the mayor's performance. In a random sample of 49 Republicans from the city, 33 approved of the mayor's performance. Find a 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance. Assume that independent simple random samples have been selected from the two populations. Round to three decimal places.
(−0.015, 0.291)
74. Complete the statement by filling in the blanks. When constructing a confidence interval, a larger sample size will _________ the margin of error and the confidence interval will be _________.
Decrease, narrower
76. Complete the statement by filling in the blanks. When constructing a confidence interval, if the level of confidence decreases, the margin of error will _________ and the confidence interval will be _________.
Decrease, narrower
80. Complete the statement by filling in the blanks. When constructing a confidence interval, if the level of confidence increases, the margin of error must _____ and the confidence interval will be _____.
Increase; wider.
