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Mind On Statistics 4th Edition David D Busch, Jessica M Utts, Robert F Heckard - Solutions

Draw a tree diagram illustrating this situation, where the first set of branches represents smoking status and the second set represents “ever divorced.”
According to the U.S. Census Bureau, “only 35 percent of the foreign-born people in the United States in 1997 were naturalized citizens, compared with 64 percent in 1970”(Sacramento Bee, October 15, 1999, p. A1).a. What is the probability that two randomly selected foreign-born people in the
Recall that the Empirical Rule in Chapter 2 stated that for bell-shaped distributions, about 68% of the values fall within one standard deviation of the mean. The heights of women at a large university are approximately bell-shaped, with a mean of 65 inches and standard deviation of 2.5 inches. Use
The 2007 Working Group on California Earthquake Probabilities reported that “the likelihood of [an earthquake in California] of magnitude 7.5 or greater in the next 30 years is 46%.” The report noted that “[t]he final forecast is a sophisticated integration of scientific fact and expert
About one-third of all adults in the United States have type O blood. If three randomly selected adults donate blood, find the probability of each of the following events.a. All three are type O.b. None of them is type O.c. Two out of the three are type O.
Recall from Chapter 2 that the median of a dataset is the value with at least half of the observations at or above it and at least half of the observations at or below it. Suppose that four individuals are randomly selected with replacement from a large class and asked how many hours they studied
Refer to Exercises 7.95, 7.96, and 7.97. Given that a randomly chosen student receives an A grade, what is the probability that he or she attended class regularly?
Refer to Exercises 7.95 and 7.96. Construct a hypothetical hundred thousand table for this situation.
Refer to Exercise 7.95. Draw a tree diagram, and use it to find the overall percent who receive As.
A professor has noticed that even though attendance is not a component of the grade for his class, students who attend regularly obtain better grades. In fact, 40% of those who attend regularly receive As in the class, while only 10% of those who do not attend regularly receive As. About 70% of
In Chapter 4, we learned that when there is no relationship between two categorical variables in a population, a “statistically significant” relationship will appear in 5% of the samples from that population, over the long run. Suppose that two researchers independently conduct studies to see
New spark plugs have just been installed in a small airplane with a four-cylinder engine. For each spark plug, the probability that it is defective and will fail during its first 20 minutes of flight is 1/10,000, independent of the other spark plugs.a. For any given spark plug, what is the
Refer to Exercise 7.91. A psychologist has noticed that“Teachers” and “Rationalists” get along particularly well with each other, and she thinks that they tend to marry each other. One of her colleagues disagrees and thinks that the types of spouses are independent of each other.a. If the
A psychological test identifies people as being one of eight types. For instance, Type 1 is “Rationalist” and applies to 15% of men and 8% of women. Type 2 is “Teacher” and applies to 12% of men and 14% of women. Each person fits one and only one type.a. What is the probability that a
Answer Thought Question 7.8 on page 250.
Answer Thought Question 7.7 on page 245.
Do you think that all coincidences can be explained by random events? Explain why or why not, using probability as the focus of your explanation. (There is no correct answer;your reasoning is what counts.)
Suppose that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse’s occupation, and so on.For simplicity, assume that the probability that your details
Give an example of a coincidence that has occurred in your life. Using the material from this chapter, try to approximate the probability of exactly that event happening. Discuss whether the answer convinces you that something very odd happened to you.
Tomorrow morning when you first arise, pick a three-digit number (anything from 000 to 999). You can choose randomly or simply decide what number you want to use. As you go through the day, note whether you encounter that number. It could be in a book, on a license plate, in a newspaper or
A friend, quite upset, calls you because she had a dream that a building had been bombed and she was helping to search for survivors. The next day, a terrorist bombed an embassy building in another country. Your friend is convinced that her dream was a warning and that she should have told someone
A friend has three boys and would like to have a girl. She explains to you that the probability that her next baby will be a girl is very high because the law of averages says that she should have half of each and she already has three boys. Is she correct? Explain.
Give an example of a situation in which the gambler’s fallacy would not apply because the events are not independent.
Suppose that there are 30 people in your statistics class and you are divided into 15 teams of 2 students each.You happen to mention that your birthday was last week, upon which you discover that your teammate’s mother has the same birthday you have (month and day, not necessarily year). Assume
A rare disease occurs in about 1 out of 1000 people who are similar to you. A test for the disease has sensitivity of 95% and specificity of 90%.a. Create a hypothetical one hundred thousand table illustrating this situation, where the row categories are disease (yes, no) and the column categories
The University of California at Berkeley’s Wellness Encyclopedia (1991) contains the following statement in its discussion of HIV testing: “In a high-risk population, virtually all people who test positive will truly be infected, but among people at low risk the false positives will outnumber
Using material from Section 7.7, explain what is wrong with the following statement: “The probability that you will win the million dollar lottery is about the same as the probability that you will give birth to quintuplets.”
Which of the following sequences resulting from tossing a fair coin five times is most likely: HHHHH, HTHHT, or HHHTT? Explain your answer.
The Pap smear is a screening test to detect cervical cancer.Estimate the sensitivity and specificity of the test if a study of 200 women with cervical cancer resulted in 160 testing positive, and in another 200 women without cervical cancer, 4 tested positive.
In tossing a fair coin 10 times, if the first nine tosses resulted in all tails, will the chance be greater than .5 that the tenth toss will turn up heads? Explain.
Janice has noticed that on her drive to work, there are several things that can slow her down. First, she hits a red light with probability .3. If she hits the red light, she also has to stop for the commuter train with probability .4, but if she doesn’t hit the red light, she has to stop with
Suppose that in a state lottery game players choose three digits, each from the set 0 to 9, as they do in many state lottery games. But for this game, what counts is the sum of the three chosen digits. The state selects a winning sum from the possibilities 0 (0 0 0) to 27 (9 9 9) by randomly
Refer to Example 7.30 (p. 244). Suppose that the probability of a correct guess each time is .40.a. Explain how you would simulate this situation.b. Carry out the simulation, and estimate the probability that a participant will be identified as gifted.
Refer to Example 7.30 (p. 244). Explain how you would change the simulation procedure if the assumption was that everyone was randomly guessing, so that the probability of a correct guess was .20 each time.
Refer to the Minitab simulation results given on pages 244–245 for Example 7.30. What is the estimated probability that a participant would guess four or more correctly?
Refer to Example 7.29 (p. 243) and use the results given in Table 7.3 to estimate probabilities of the following outcomes:a. Prize 4 is received at least three times.b. Prize 4 is received at least three times given that the full collection of all four prizes was not received.c. Prize 4 is received
The observed risk of an accident per month at a busy intersection without any stoplights was 1%. The potential benefit of adding a stoplight was studied by using a computer simulation modeling the typical traffic flow for a month at that intersection. In 10,000 repetitions, a total of 50 simulated
Five fair dice were tossed, and the sum of the resulting tosses was recorded. This process was repeated 10,000 times using a computer simulation. The number of times the sum of the five tosses equaled 27 was 45. What is the estimated probability that the sum of the five dice will be 27?
Two students each use a random number generator to pick an integer between 1 and 7. What is the probability that they pick the same number?
In an Italian breakfast café, a waitress has observed that 80% of her customers order coffee and 25% of her customers order both biscotti and coffee. Define A a randomly selected customer orders coffee.B a randomly selected customer orders biscotti.
In a computer store, 30% (.3) of the computers in stock are laptops and 70% (.7) are desktops. Five percent (.05) of the laptops are on sale, while 10% (.1) of the desktops are on sale. Use a tree diagram to determine the percentage of the computers in the store that are on sale.
Refer to Exercise 7.56.a. Create a tree diagram for this situation.b. Use the tree diagram in part (a) to determine what percentage of the class are seniors.
In a large general education class, 60% (.6) are science majors and 40% (.4) are liberal arts majors. Twenty percent(.2) of the science majors are seniors, while 30% (.3) of the liberal arts majors are seniors.a. If there are 100 students in the class, how many of them are science majors?b. If
A public library carries 50 magazines, each of which focuses on either news or sports. Thirty of the magazines focus on news and the remaining 20 focus on sports.Among the 30 news magazines, 20 include international news and 10 include national, state, or local news only.Among the 20 sports
A robbery has been committed in an isolated town.Witnesses all agree that the criminal was driving a red pickup truck and had blond hair. Evidence at the scene indicates that the criminal also smoked cigarettes. Police determine that 1/50 of the vehicles in town are red pickup trucks, 30% of the
A raffle is held in a club in which 10 of the 40 members are good friends with the president. The president draws two winners.a. If the two winners are drawn with replacement, what is the probability that a friend of the president wins each time?b. If the two winners are drawn without replacement,
Harold and Maude plan to take a cruise together, but they live in separate cities. The cruise departs from Miami, and they each book a flight to arrive in Miami an hour before they need to be on the ship. Their travel planner explains that Harold’s flight has an 80% chance of making it on time
In Example 7.15, we found that the probability that a woman with two children either has two girls or two boys is .5002. What is the probability that she has one child of each sex?
Refer to Exercise 7.49. In this exercise, another method is used for finding the probability that at least one of two unrelated strangers shares your birth month.a. What is the probability that the first stranger shares your birth month?b. What is the probability that the second stranger shares
In Example 7.17. (p. 233), we found the probability that both of two unrelated strangers share your birth month. In this exercise, we find the probability that at least one of the two strangers shares your birth month. Assume that all 12 months are equally likely.a. What is the probability that the
In each situation, explain whether the selection is made with replacement or without replacement.a. The two football teams selected to play in the Rose Bowl in a given year.b. The cars stopped by the police for speeding in five consecutive mornings on the same stretch of highway.c. The winning
In each situation, explain whether the selection is made with replacement or without replacement.a. The three digits in the lottery in Example 7.2. (p. 223).b. The three students selected to answer questions in Case Study 7.1. (p. 220).c. Five people selected for extra security screening while
In a recent election, 55% of the voters were Republicans, and 45% were not. Of the Republicans, 80% voted for Candidate X, and of the non-Republicans, 10% voted for Candidate X.Consider a randomly selected voter. Define A Voter is Republican.B Voted for Candidate X.a. Write values for P(A), P(AC),
Julie is taking English and history. Suppose that at the outset of the term, her probabilities for getting As are P(grade of A in English class) .70.P(grade of A in history class) .60.P(grade of A in both English and history classes) .50.a. Are the events “grade of A in English class” and
Refer to Exercise 7.43. Find the following probabilities:a. P(A)b. P(B)c. P(A and B)d. P(A or B)e. P(A and C)f. P(A or C)
A popular lottery game is one in which three digits from 0 to 9 are chosen, so the winning number can be any of the 1000 numbers from 000 to 999. Define:A the first digit is odd B the first digit is even C the second digit is odda. State two of these events that are mutually exclusive.b. State two
Refer to Exercise 7.41. Now suppose you meet two new friends independently, and ask each of them on what day of the week they were born.a. What is the probability that the first friend was born on a Friday?b. What is the probability that both friends were born on a Friday?c. What is the probability
Suppose that people are equally likely to have been born on any day of the week. You meet a new friend, and ask her on what day of the week she was born.a. List the simple events in the sample space.b. What is the probability that she was born on a weekend(Saturday or Sunday)?
Two fair coins are tossed. Define A Getting a head on the first coin B Getting a head on the second coin A and B Getting a head on both the first and second coins A or B Getting a head on the first coin, or the second coin, or both coinsa. Find P(A) the probability of A.b. Find P(B) the probability
A fair coin is tossed three times. The event “A getting all heads” has probability 1/8.a. Describe in words what the event AC is.b. What is the probability of AC?
Two fair dice are rolled. The event “A getting the same number on both dice” has probability 1/6.a. Describe in words what the event AC is.b. What is the probability of AC?
Refer to Case Study 7.1. Define C1, C2, and C3 to be the events that Alicia is called on to answer questions 1, 2, and 3, respectively.a. Based on the physical situation used to select students, what is the (unconditional) probability of each of these events? Explain.b. What is the conditional
Refer to Exercise 7.34. Which method of finding probabilities do you think was used to find the “90 percent chance”and “37 percent chance”? Explain.
Refer to Exercise 7.34. Suppose that an American woman is randomly selected. Are her age and her fertility status independent? Explain.
According to Krantz (1992, p. 102), “[In America] women between the ages of 20 and 24 have a 90 percent chance of being fertile while women between 40 and 44 have only a 37 percent chance of bearing children [i.e., being fertile].”Define appropriate events, and write these statements as
Refer to Exercise 7.32. Suppose that a student is asked to choose a number from 1 to 10. Define event A to be that the student chooses the number 5, and event B to be that the student chooses an even number.a. What is P(A and B)?b. Are events A and B independent? Explain how you know.c. Are events
When 190 students were asked to pick a number from 1 to 10, the number of students selecting each number were as follows:a. What is the approximate probability that someone asked to pick a number from 1 to 10 will pick the number 3?b. What is the approximate probability that someone asked to pick a
Use the information given in Case Study 7.1. and the “physical assumption” method of assigning probabilities to argue that on any given day, the probability that Alicia has to answer one of the three questions is 3/50.
Refer to Exercise 7.29, in which a red die and a green die are each tossed once. Explain whether the following pairs of events are mutually exclusive, independent, both, or neither:a. A red die and green die sum to 4; B red die is a 3.b. A red die and green die sum to 4; B red die is a 4.
When a fair die is tossed, each of the six sides (numbers 1 to 6) is equally likely to land face up. Two fair dice, one red and one green, are tossed. Explain whether the following pairs of events are mutually exclusive, independent, both, or neither:a. A red die is a 3; B red die is a 6.b. A red
Jill and Laura have lunch together. They flip a coin to decide who pays for lunch and then flip a coin again to decide who pays the tip. Define a possible outcome to be who pays for lunch and who pays the tip, in order—for example, “Jill, Jill.”a. List the simple events in the sample space.b.
Refer to Example 7.10 (p. 229), in which you and your friend Vanessa enter a drawing for a free lunch in Week 1 and again in Week 2. Events defined were A you win in Week 1, B Vanessa wins in Week 1, C Vanessa wins in Week 2.a. Are events B and C independent? Explain.b. Suppose that after Week 1,
Suppose that events A and B are mutually exclusive with P(A) 1/2 and P(B) 1/3.a. Are A and B independent events? Explain how you know.b. Are A and B complementary events? Explain how you know.
Suppose that A, B, and C are all disjoint possible outcomes for the same random circumstance. Explain whether each of the following sets of probabilities is possible.a. P(A) 1/3, P(B) 1/3, P(C) 1/3.b. P(A) 1/2, P(B) 1/2, P(C) 1/4.c. P(A) 1/4, P(B) 1/4, P(C) 1/4.
A penny and a nickel are each tossed once. Explain whether the outcomes for the two coins are:a. Independent events.b. Complementary events.c. Mutually exclusive events.
Remember that the event AC is the complement of the event A.a. Are A and AC mutually exclusive? Explain.b. Are A and AC independent? Explain.
Refer to Exercise 7.21. in which the number of days a randomly selected student exercised in the previous week is recorded. List the simple events that make up each of these events:a. The student exercised on at least 5 days.b. The student exercised on at most 2 days.c. The student did not exercise
Suppose that we randomly select a student and record how many days in the previous week the student exercised for at least half an hour. Make a list of the simple events in the sample space.
A student wants to send a bouquet of roses to her mother for Mother’s Day. She can afford to buy only two types of roses and decides to randomly pick two different varieties from the following four choices: Blue Bell, Yellow Success, Sahara, and Aphrodite. Label these varieties B, Y, S, A.a. Make
Refer to Example 7.5 (p. 224). What is the probability that a randomly selected child who slept in darkness would develop some degree of myopia?
Every day, John buys a lottery ticket with the number 777 for the lottery described in Example 7.2. He has played 999 times and has never won. He reasons that since tomorrow will be his 1000th time and the probability of winning is 1/1000, he will have to win tomorrow. Explain whether John’s
Alicia’s statistics class meets 50 times during the semester, and each time it meets, the probability that she will be called on to answer the first question is 1/50. Does this mean that Alicia will be called on to answer the first question exactly once during the semester? Explain.
Give an example of a situation for which a probability statement makes sense but for which the relative frequency interpretation could not apply, such as the probability given by Carl Sagan for an asteroid hitting Earth.
A computer solitaire game uses a standard 52-card deck and randomly shuffles the cards for play. Theoretically, it should be possible to find optimal strategies for playing and then to compute the probability of winning based on the best strategy. Not only would this be an extremely complicated
Casino games often use a fair die that has six sides with 1 to 6 dots on them. When the die is tossed or rolled, each of the six sides is equally likely to come out on top.Using the physical assumption that the die is fair, determine the probability of each of the following outcomes for the number
Refer to Exercise 7.5. Suppose that Robin wants to find the probability associated with the outcomes in the random circumstances contained in the story. Identify one of the circumstances, and explain how she could determine the probabilities associated with its outcomes.
Explain which interpretation of probability (relative frequency or personal) applies to each of these statements and how you think the probability was determined.a. According to Krantz (1992, p. 161), the probability that a randomly selected American will be injured by lightning in a given year is
Which interpretation of probability (relative frequency or personal) applies to each of the following situations? If it’s the relative frequency interpretation, explain which of the methods listed in the “In Summary” box at the end of Section 7.2 applies.a. If a spoon is tossed 10,000 times
A car dealer has noticed that 1 out of 25 new-car buyers returns the car for warranty work within the first month.a. Write a sentence expressing this fact as a proportion.b. Write a sentence expressing this fact as a percent.c. Write a sentence expressing this fact as a probability.
Suppose that you live in a city that has 125,000 households with telephones and a polling organization randomly selects 1000 of them to phone for a survey. What is the probability that your household will be selected?
Is each of the following values a legitimate probability value?Explain any “no” answers.a. .50b. .00c. 1.00d. 1.25e. 2.25
Give an example of a random circumstance in which:a. The outcome is not determined until we observe it.b. The outcome is already determined, but our knowledge of it is uncertain.
Answer Thought Question 7.2 on page 221.
Identify three random circumstances in the following story, and give the possible outcomes for each of them:It was Robin’s birthday and she knew she was going to have a good day. She was driving to work, and when she turned on the radio, her favorite song was playing.Besides, the traffic light at
Find information on a random circumstance in the news.Identify the circumstance and possible outcomes, and assign probabilities to the outcomes. Explain how you determined the probabilities?
Jan is a member of a class with 20 students that meets daily.Each day for a week (Monday to Friday), a student in Jan’s class is randomly selected to explain how to solve a homework problem. Once a student has been selected, he or she is not selected again that week. If Jan was not one of the
Answer Thought Question 7.1 on page 221.
According to a U.S. Department of Transportation website(http://www.bts.gov/press_releases/2010/dot045_10/html/dot045_10.html), 78.7% of domestic flights flown by the top 18 U.S. airlines in January 2010 arrived on time. Represent this in terms of a random circumstance and an associated probability.
In an experiment done at an English university, 64 students held their hands in ice water for as long as they could while repeating a swear word of their choice. The same students also held their hands in ice water for as long as they could while repeating a neutral word. For each condition, the
Refer to the first observational study described in Case Study 6.1 (p. 193). In the study, a link was found between tooth decay and exposure to lead for 24,901 children. Give an example of a possible confounding variable in addition to those described in the text. Explain why it could be a

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