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statistics
elementary statistics in social research
Elementary Statistics Picturing The World 7th Global Edition Betsy Farber, Ron Larson - Solutions
It costs \($12\) to bet on a horse race. The horse has a 16 chance of winning and a 1/3 chance of placing 2nd or 3rd. You win \($42\) if the horse wins and receive your money back if the horse places 2nd or 3rd.Find the expected net gain to the player for one play of the game.
Playing a gambling game costs $10. The table shows the probability of winning various prizes on the game.Find the expected net gain to the player for one play of the game. Prize Probability 1 $200 400 1 $100 100 1 $50 25
In a recent season, hockey player Evgeni Malkin scored 27 goals in 57 games he played. Assume that his goal production stayed at that level for the next season. Find the probability that he would get his first goal (a) in the first game of the season, (b) in the second game of the season, (c)
A study found that the smartphones made by a certain manufacturer had a failure rate of 43%. Four smartphones made by this manufacturer are selected at random. Find the probability that the fourth smartphone is the first one to have a failure.
The mean number of accidents per month at a certain intersection is three.What is the probability that in any given month four accidents will occur at this intersection?
A population count shows that the average number of rabbits per acre living in a field is 3.6. Use a table to find the probability that seven rabbits are found on any given acre of the field.
Determine whether each experiment is a binomial experiment. If it is, specify the values of n, p, and q, and list the possible values of the random variable x.If it is not, explain why.1. A certain surgical procedure has an 85% chance of success. A doctor performs the procedure on eight patients.
Rotator cuff surgery has a 90% chance of success. The surgery is performed on three patients. Find the probability of the surgery being successful on exactly two patients.
In a survey, U.S. adults were asked to identify which social media platforms they use. The results are shown in the figure. Six adults who participated in the survey are randomly selected and asked whether they use the social media platform Facebook. Construct a binomial probability distribution
A survey found that 26% of U.S. adults believe there is no difference between secured and unsecured wireless networks. (A secured network uses barriers, such as firewalls and passwords, to protect information; an unsecured network does not.) You randomly select 100 adults. What is the probability
A survey found that 17% of U.S. adults say that Google News is a major source of news for them. You randomly select four adults and ask them whether Google News is a major source of news for them. Find the probability that(1) exactly two of them respond yes, (2) at least two of them respond yes,
About 10% of workers (ages 16 years and older) in the United States commute to their jobs by carpooling. You randomly select eight workers. What is the probability that exactly four of them carpool to work? Use a table to find the probability.
Sixty-two percent of cancer survivors are ages 65 years or older. You randomly select six cancer survivors and ask them whether they are 65 years of age or older. Construct a probability distribution for the random variable x. Then graph the distribution.
In Pittsburgh, Pennsylvania, about 56% of the days in a year are cloudy. Find the mean, variance, and standard deviation for the number of cloudy days during the month of June. Interpret the results and determine any unusual values.
A person is required to toss 8 unbiased coins and note down the outcome of each. The random variable represents the number of heads.Determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random
You draw four cards, one at a time, from a standard deck. You note the suit and replace the card in the deck. The random variable represents the number of cards that are diamonds.Determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and
Fifty-two percent of the women in the UK play video games regularly. You randomly select seven women in the UK. Find the probability that the number of women in the UK who are gamers is(a) exactly four,(b) at least five,(c) less than four.Find the indicated probabilities. If convenient, use
Thirty-three percent of online consumers in Russia prefer to shop online using smartphones. You randomly select 12 consumers.Find the probability that the number of online consumers who purchase using smartphones is(a) exactly six,(b) more than six,(c) at most six.Find the indicated probabilities.
The official website of Major League Baseball, MLB.com, records detailed statistics about players and games. During the 2016 regular season, Dustin Pedroia of the Boston Red Sox had a batting average of 0.318. The graphs below show the number of hits he had in games in which he had different
A survey consists of asking people for their blood types (O, A, B, and AB), including whether they are Rh-positive or Rh-negative. Determine the number of outcomes and identify the sample space.
Determine the number of outcomes in each event. Then decide whether each event is simple or not. Explain your reasoning.1. For quality control, you randomly select a machine part from a batch that has been manufactured that day. Event A is selecting a specific defective machine part.2. You roll a
You are purchasing a new car. The possible manufacturers, car sizes, and colors are listed in the table.How many different ways can you select one manufacturer, one car size, and one color? Use a tree diagram to check your result. Manufacturer Car size Color Ford compact white (W) GM midsize red
The access code for a car’s security system consists of four digits. Each digit can be any number from 0 through 9.How many access codes are possible when 1. each digit can be used only once and not repeated?2. each digit can be repeated?3. each digit can be repeated but the first digit cannot be
You roll a six-sided die. Find the probability of each event.1. Event A: rolling a 3 2. Event B: rolling a 7 3. Event C: rolling a number less than 5
A company is conducting an online survey of randomly selected U.S. adults to determine how they read books during the past year, if at all. So far, 1490 adults have been surveyed. The pie chart shows the results. (Note that digital books include ebooks as well as audio books.) What is the
A company is conducting a phone survey of randomly selected individuals to determine the ages of social networking site users. So far, 975 social networking site users have been surveyed. The frequency distribution at the right shows the results. What is the probability that the next user surveyed
Classify each statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.1. The probability that you will get an A on your next test is 0.9.2. The probability that a voter chosen at random will be younger than 35 years old is 0.3.3.
The frequency distribution from Example 7 is shown below. Find the probability of randomly selecting a social networking site user who is not 23 to 35 years old.Data from Example 7A company is conducting a phone survey of randomly selected individuals to determine the ages of social networking site
A probability experiment consists of tossing a coin and spinning the spinner shown at the left. The spinner is equally likely to land on each number. Use a tree diagram to find the probability of each event.1. Event A: tossing a tail and spinning an odd number 2. Event B: tossing a head or
Your college identification number consists of eight digits. Each digit can be 0 through 9 and each digit can be repeated. What is the probability of getting your college identification number when randomly generating eight digits?
A restaurant offers a $20 dinner special that lets you choose from 8 appetizers, 11 entrées, and 7 desserts. How many different meals are available when you select an appetizer, an entrée, and a dessert?
A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of five digits. The first digit cannot be zero or nine and the last digit must be a multiple of 3. How many different codes are available?
Assuming that no questions are left unanswered, in how many ways can a ten-question yes or no quiz be answered?
Event C: rolling a number less than 3A probability experiment consists of rolling a 12-sided die, numbered 1 to 12. Find the probability of the event.
Event D: rolling a number more than 11 A probability experiment consists of rolling a 12-sided die, numbered 1 to 12. Find the probability of the event.
Event E: rolling a number divisible by 4 A probability experiment consists of rolling a 12-sided die, numbered 1 to 12. Find the probability of the event.
What is the probability that the next household asked does not have a car?A polling organization is asking a sample of U.K. households how many cars they have. The frequency distribution at the left shows the results. Use the frequency distribution. Number of Response cars, f None 960 One 1800 Two
What is the probability that the next household asked has one car?A polling organization is asking a sample of U.K. households how many cars they have. The frequency distribution at the left shows the results. Use the frequency distribution. Number of Response cars, f None 960 One 1800 Two 920
The probability that a randomly selected number from 1 to 50 is divisible by 4 is 0.24.Classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.
You think that a candidate’s probability of winning the next election is about 0.65.Classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.
According to a survey, the probability that an adult chosen at random watches a movie every day is about 0.60.Classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.
An access code consists of three digits. Each digit can be any number from 0 through 9, and each digit can be repeated.(a) What is the probability of randomly selecting the correct access code on the first try?(b) What is the probability of not selecting the correct access code on the first try?
An access code consists of two characters. Each character can be any alphabet from A through Z, and each alphabet can be repeated.(a) What is the probability of randomly selecting the correct access code on the first try?(b) What is the probability of not selecting the correct access code on the
The probability of randomly choosing a cricket player who also played for his school team. (Assume that you are choosing from the population of all cricket players.)Write a statement that represents the complement of the probability.
1. Two cards are selected in sequence from a standard deck of 52 playing cards. Find the probability that the second card is a queen, given that the first card is a king. (Assume that the king is not replaced.)2. The table at the left shows the results of a survey in which 2276 social media users
Determine whether the events are independent or dependent.1. Selecting a king (A) from a standard deck of 52 playing cards, not replacing it, and then selecting a queen (B) from the deck 2. Tossing a coin and getting a head (A), and then rolling a six-sided die and obtaining a 6 (B).3. Driving
1. Two cards are selected, without replacing the first card, from a standard deck of 52 playing cards. Find the probability of selecting a king and then selecting a queen.2. A coin is tossed and a die is rolled. Find the probability of tossing a head and then rolling a 6.
For anterior cruciate ligament (ACL) reconstructive surgery, the probability that the surgery is successful is 0.95.1. Find the probability that three ACL surgeries are successful.2. Find the probability that none of the three ACL surgeries are successful.3. Find the probability that at least one
In a recent year, there were 18,187 U.S. allopathic medical school seniors who applied to residency programs and submitted their residency program choices. Of these seniors, 17,057 were matched with residency positions, with about 79.2% getting one of their top three choices. Medical students rank
The table shows the results of a survey in which 300 managers and 300 executives aged 25 to 50 were asked if they go for annual leisure trips.(a) Find the probability that a randomly selected employee goes for leisure trips, given that the employee is an executive.(b) Find the probability that a
Returning a library book before the due date and getting a new book issued.Determine whether the events are independent or dependent. Explain your reasoning.
A study found that women have more cone cells, but they do not perceive color differently from men.Identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.
A study found that eating a few pieces of chocolate each week can improve your cardiovascular health.Identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.
Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a king and then selecting a queen.Use the Multiplication Rule.
A coin is tossed and a die is rolled. Find the probability of tossing a head and then rolling a number lesser than 3.Use the Multiplication Rule.
An HR consultant gives an applicant a 75% chance of getting a job after registering with his agency. If the applicant gets a job, then there is a 60% possibility that he would be satisfied and would not resign within a year. Find the probability that the applicant gets the job and does not resign
\(P(A)=73 \%, P\left(A^{\prime}\right)=27 \%, P(B \mid A)=46 \%\), and \(P\left(B \mid A^{\prime}\right)=52 \%\)According to Bayes' Theorem, the probability of event A, given that event B has occurred, is \(P(A \mid B)=\frac{P(A) \cdot P(B \mid A)}{P(A) \cdot P(B \mid A)+P\left(A^{\prime}\right)
\(P(A)=12 \%, P\left(A^{\prime}\right)=88 \%, P(B \mid A)=66 \%\), and \(P\left(B \mid A^{\prime}\right)=19 \%\)According to Bayes' Theorem, the probability of event A, given that event B has occurred, is \(P(A \mid B)=\frac{P(A) \cdot P(B \mid A)}{P(A) \cdot P(B \mid A)+P\left(A^{\prime}\right)
Determine whether the events are mutually exclusive. Explain your reasoning.1. Event A: Roll a 3 on a die.Event B: Roll a 4 on a die.2. Event A: Randomly select a male student.Event B: Randomly select a nursing major.3. Event A: Randomly select a blood donor with type O blood.Event B: Randomly
1. You select a card from a standard deck of 52 playing cards. Find the probability that the card is a 4 or an ace.2. You roll a die. Find the probability of rolling a number less than 3 or rolling an odd number.
The frequency distribution shows volumes of sales (in dollars) and the number of months in which a sales representative reached each sales level during the past three years. Using this sales pattern, find the probability that the sales representative will sell between \($75,000\) and \($124,999\)
A blood bank catalogs the types of blood, including whether it is Rh-positive or Rh-negative, given by donors during the last five days. The number of donors who gave each blood type is shown in the table.1. Find the probability that a donor selected at random has type O or type A blood.2. Find the
Use the figure at the right to find the probability that a randomly selected draft pick is not a running back or a wide receiver. NFL Rookies A breakdown by position of the 253 players picked in the 2016 NFL draft: Offensive tackles Guards Quarterbacks Running backs 15 -23 17 7 Centers Tight ends
Event A: Randomly select a student who studies for more than 5 hours daily.Event B: Randomly select a student who studies for less than 2 hours daily.Determine whether the events are mutually exclusive. Explain your reasoning.
Event A: Randomly select a female badminton player.Event B: Randomly select a badminton player who is 25 years old.Determine whether the events are mutually exclusive. Explain your reasoning.
A class has 60 students. Of these, 35 students are male and 20 students know how to play a musical instrument. Of the male students, five can play musical instruments. Find the probability that a randomly selected student is male or can play a musical instrument.
Of the mobile phones produced by a company, 97% do not have a poor battery life, 95% do not have a corrupt operating system, and 93.5% do not have a poor battery life and do not have a corrupt OS. Find the probability that a randomly selected mobile does not have a poor battery life or a corrupt OS.
Of the cameras produced by a company, 8% have a flash problem, 12% have a focus malfunction, and 0.9% have both a flash issue and a focus malfunction. Find the probability that a randomly selected camera has a flash problem or a focus malfunction.
You roll a die. Find the probability of each event.(a) Rolling a 6 or a number greater than 4(b) Rolling a 2 or a prime number(c) Rolling a number less than 5 or an odd number
A card is selected at random from a standard deck of 52 playing cards. Find the probability of each event.(a) Randomly selected a black suit or a king(b) Randomly selected a diamond or a face card(c) Randomly selected a club or a diamond
The estimated percent distribution of the U.S. population for 2025 is shown in the pie chart. Find the probability of each event.(a) Randomly selecting someone who is under 5 years old(b) Randomly selecting someone who is 45 years or over(c) Randomly selecting someone who is not 65 years or over(d)
Marijuana Use The percent of college students’ marijuana use for a sample of 95,761 students is shown in the pie chart. Find the probability of each event.(a) Randomly selecting a student who never used marijuana(b) Randomly selecting a student who used marijuana(c) Randomly selecting a student
The table shows the result of a survey that asked 4087 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.(a) The person is female or wears both contacts and glasses.(b) The person is male or wears neither of the two.(c)
The objective of a 9 × 9 Sudoku number puzzle is to fill the grid so that each row, each column, and each 3 × 3 grid contain the digits 1 through 9. How many different ways can the first row of a blank 9 × 9 Sudoku grid be filled?
Find the number of ways of forming four-digit codes in which no digit is repeated.
Each year, 33 race cars start the Indianapolis 500. How many ways can the cars finish first, second, and third?
A building contractor is planning to develop a subdivision. The subdivision is to consist of 6 one-story houses, 4 two-story houses, and 2 split-level houses.In how many distinguishable ways can the houses be arranged?
A state’s department of transportation plans to develop a new section of interstate highway and receives 16 bids for the project. The state plans to hire four of the bidding companies. How many different combinations of four companies can be selected from the 16 bidding companies?
A student advisory board consists of 17 members. Three members will be chosen to serve as the board’s chair, secretary, and webmaster. Each member is equally likely to serve in any of the positions. What is the probability of randomly selecting the three members who will be chosen for the board?
Find the probability of being dealt 5 diamonds from a standard deck of 52 playing cards.
A food manufacturer is analyzing a sample of 400 corn kernels for the presence of a toxin. In this sample, three kernels have dangerously high levels of the toxin.Four kernels are randomly selected from the sample. What is the probability that exactly one kernel contains a dangerously high level of
7C5 = 7C2 Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
9P5 Perform the indicated calculation.
14P3 Perform the indicated calculation.
8C3 Perform the indicated calculation.
3P2/13P1 Perform the indicated calculation.
You have won nine different trophies. How many different ways can you arrange the trophies side by side on a shelf?
The starting lineup for a baseball team in an international match is 12 players. How many different batting orders are possible using the starting lineup?
There are 20 finalists in an inter-school dancing competition. The top three students will receive prize money. How many ways can the dancers finish first through third?
At a blood drive, 5 donors with type O+ blood, 7 donors with type A+ blood, and 3 donors with type B+ blood are in line. In how many distinguishable ways can the donors be in line?
A class has 50 students. In how many different ways can five students form a group to work on a class project? (Assume the order of the students is not important.)
A food inspection office is analyzing milk samples from 75 vendors for adulteration. The milk supplied by six of the vendors have high levels of adulteration. Five vendors are randomly selected from the sample. Using technology, how many ways could two vendors who put adulterants in milk and three
The Council of Australian governments has 10 members. Two members are chosen to serve as the executive committee members. Each council member is equally likely to serve in these positions. What is the probability of randomly selecting the committee members?
A salad shop offers eleven sauces. No sauce is used more than once. What is the probability that the sauces in a four-sauce salad are mayonnaise, mustard, barbecue, and red chili?
In a state lottery, you must correctly select 7 numbers (in any order) out of 70 to win the top prize. You purchase one lottery ticket. What is the probability that you will win the top prize?
A company that has 200 employees chooses a committee of 5 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected.(a) Use technology to find the number of ways 5 employees can be chosen from 200.(b) Use technology to find the number of
Find the probability of choosing six second-shift workers.A warehouse employs 24 workers on first shift, 17 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment.
Probability affects decisions when the weather is forecast, when medications are selected, and even when players are selected for professional sports teams.Although intuition is often used for determining probabilities, you will be better able to assess the likelihood of an event by applying the
A student has to choose a menu consisting of a soup, a sandwich and a dessert from choices of 3 soups, 5 sandwiches and 2 desserts. How many ways can the student choose the menu?Use the Fundamental Counting Principle.
The registration numbers of candidates appearing for an examination have four letters followed by three digits. Assuming that any letter or digit can be used, how many different registration numbers are possible?Use the Fundamental Counting Principle.
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