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elementary statistics
Elementary Statistics Picturing The World 5th Edition Ron Larson, Betsy Farber - Solutions
The U.S. unemployment rate over a 12-year period is given. Use the data to construct a time series chart. (Source: U.S. Bureau of Labor Statistics) Year 1998 1999 2000 2001 2002 2003 Unemployment rate 4.5 4.2 4.0 4.7 5.8 6.0 Year 2004 2005 2006 2007 2008 2009 Unemployment rate 5.5 5.1 4.6 4.6 5.8
The following are the heights (in feet) and the number of stories of nine notable buildings in Houston. Use the data to construct a scatter plot. What type of pattern is shown in the scatter plot? (Source: Emporis Corporation) Height (in feet) 992 780 762 756 741 732 714 662 579 Number of stories
Make a dot plot of the data set.
Make a stem-and-leaf plot of the data set. Use one line per stem.
Make an ogive of the data set using six classes.
Make a frequency distribution of the data set with six classes and draw a frequency polygon.
Make a relative frequency histogram of the data set using seven classes. In Exercises 5 and 6, use the following data set. The data represent the number of rooms reserved during one night’s business at a sample of hotels. 153 104 118 166 89 104 100 79 93 96 116 94 140 84 81 96 108 111 87 126 101
Make a frequency histogram of the data set using seven classes.
Make a relative frequency histogram using the frequency distribution in Exercise 1.Then determine which class has the greatest relative frequency and which has the least relative frequency. In Exercises 3 and 4, use the following data set. The data represent the actual liquid volumes (in ounces) in
Make a frequency distribution of the data set using five classes. Include the class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies.
What is the standard deviation of the difference in their scores?
The mean annual salary of employees at a company is $36,000 with a variance of 15,202,201.At the end of the year, each employee receives a $2000 bonus and a 4% raise (based on salary).What is the standard deviation of the new salaries?
The mean annual salary of employees at a company is $36,000. At the end of the year, each employee receives a $1000 bonus and a 5% raise (based on salary). What is the new mean annual salary (including the bonus and raise) of the employees?
Students The enrollments (in thousands) for grades 1 through 8 in the United States for a recent year (Source: US National Center for Education Statistics) Grade 1 2 3 4 5 6 7 8 Enrollment 3750 3640 3627 3585 3601 3660 3715 3765
Computers The number of computers per household in a small town Computers 0 1 2 3 Households 300 280 95 20
A charity organization is selling $5 raffle tickets as part of a fund-raising program. The first prize is a trip to Mexico valued at $3450, and the second prize is a weekend spa package valued at $750. The remaining 20 prizes are $25 gas cards. The number of tickets sold is 6000. SC In Exercises 47
In American roulette, the wheel has the 38 numbers 00, 0, 1, 2, , 34, 35, and 36 marked on equally spaced slots. If a player bets $1 on a number and wins, then the player keeps the dollar and receives an additional 35 dollars. Otherwise, the dollar is lost.
Unusual Values A person randomly chooses a World Series in which eight games were played and claims that this is an unusual event. Use the information in Exercise 28 to determine if this person is correct.Explain you reasoning. Games of Chance In Exercises 45 and 46, find the expected net gain to
Unusual Values A person lives in a household with three dogs and claims that having three dogs is not unusual. Use the information in Exercise 27 to determine if this person is correct. Explain your reasoning.
Finding Probabilities Use the probability distribution you made for Exercise 28 to find the probability of randomly selecting a World Series that consisted of (a) four games, (b) at least five games, and (c) between four and six games, inclusive.
Finding Probabilities Use the probability distribution you made for Exercise 27 to find the probability of randomly selecting a household that has (a) fewer than two dogs, (b) at least one dog, and (c) between one and three dogs, inclusive.
Carpooling The histogram shows the distribution of carpooling by the number of cars per household. (Adapted from Federal Highway Administration)
Household Size The histogram shows the distribution of household sizes in the United States for a recent year. (Adapted from U.S. Census Bureau)
Car Occupancy The histogram shows the distribution of occupants in cars crossing the Tacoma Narrows Bridge in Washington each week. (Adapted from Washington State Department of Transportation)
Hurricanes The histogram shows the distribution of hurricanes that have hit the U.S. mainland by category, with 1 the weakest level and 5 the strongest. (Source: Weather Research Center) Hurricanes That Have Hit the U.S. P(x) Tacoma Narrows Bridge: Car Occupancy P(x) 0.392 0.40 0.35 0.30 0.25 0.20
911 Calls A 911 service center recorded the number of calls received per hour. The random variable x represents the number of calls per hour for one week. 0 1 2 3 4 5 6 7 Xx P(x) 0.01 0.10 0.26 0.33 0.18 0.06 0.03 0.03 Probability
Quiz Students in a class take a quiz with eight questions. The random variable x represents the number of questions answered correctly. 0 12345678 P(x) 0.02 0.02 0.06 0.06 0.08 0.22 0.30 0.16 0.08
Writing In a game of chance, what is the relationship between a "fair bet" and its expected value? Explain. Finding Expected Value In Exercises 35-40, use the probability distribution or histogram to find the (a) mean, (b) variance, (c) standard deviation, and (d) expected value of the probability
Writing The expected value of an accountant's profit and loss analysis is 0. Explain what this means.
Extracurricular Activities The number of school-related extracurricular activities per student Activities 0 1 2 3 4 5 6 7 Students 19 39 52 57 68 41 27 17
Overtime Hours The number of overtime hours worked in one week per employee Overtime hours 0 1 2 3 4 5 6 Employees 6 12 29 57 42 30 16
Camping Chairs The number of defects per batch of camping chairs inspected Defects 0 1 2 3 4 5 Batches 95 113 87 64 13 8
Televisions The number of televisions per household in a small town Televisions 0 1 2 3 Households 26 442 728 1404
Baseball The number of games played in the World Series from 1903 to 2009 (Source: Major League Baseball). Games played 4 5 6 7 8 Frequency 20 23 23 36 3
Dogs The number of dogs per household in a small town Dogs 0 1 2 3 4 5 Households 1491 425 168 48 29 14
Quality Control A quality inspector checked for imperfections in rolls of fabric for one week. The random variable x represents the number of imperfections found. x 0 1 2 3 4 5 P(x) Constructing Probability Distributions In Exercises 27–32, (a) use the frequency distribution to construct a
Tires A mechanic checked the tire pressures on each car that he worked on for one week. The random variable x represents the number of tires that were underinflated. x 0 1 2 3 4 P(x) 0.30 0.25 0.25 0.15 0.05
x 0 1 2 3 456 P(x) 0.05 ? 0.23 0.21 0.17 0.11 0.08 Identifying Probability Distributions In Exercises 25 and 26, decide whether the distribution is a probability distribution. If it is not a probability distribution, identify the property (or properties) that are not satisfied.
x 4 P(x) 0.07 0.20 0.38 ? 0.13
Blood Donations A survey asked a sample of people how many times they donate blood each year. The random variable x represents the number of donations in one year. Use the histogram to find the probability that a person selected at random from the survey’s sample donated blood (a) more than once
Employee Testing A company gave psychological tests to prospective employees.The random variable x represents the possible test scores. Use the histogram to find the probability that a person selected at random from the survey’s sample had a test score of (a) more than two and (b) less than four.
Let x represent the total number of die rolls required for an individual to roll a five.
Let x represent the amount of snow (in inches) that fell in Nome, Alaska last winter.
Let x represent the tension at which a randomly selected guitar’s strings have been strung.
Let x represent the number of messages posted each month on a social networking website.
Let x represent the number of tornadoes in the month of June in Oklahoma.
Let x represent the volume of blood drawn for a blood test.
Let x represent the length of time it takes to get to work.
Let x represent the number of books in a university library.
The annual traffic fatalities in the after being hit United States (Source: U.S. National Highway Traffic Safety Administration) Distinguishing Between Discrete and Continuous Random Variables In Exercises 13–20, decide whether the random variable x is discrete or continuous. Explain your
The distance a baseball travels
The length of time student-athletes a rock group practice each week
The attendance at concerts for
The expected value of a discrete random variable is equal to the standard deviation of the random variable. Graphical Analysis In Exercises 9–12, decide whether the graph represents a discrete random variable or a continuous random variable. Explain your reasoning.
The mean of a random variable represents the “theoretical average” of a probability experiment and sometimes is not a possible outcome.
For a random variable x, the word random indicates that the value of x is determined by chance.
In most applications, continuous random variables represent counted data, while discrete random variables represent measured data.
What is the significance of the mean of a probability distribution? True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
What is a discrete probability distribution? What are the two conditions that determine a probability distribution?
What is a random variable? Give an example of a discrete random variable and a continuous random variable. Justify your answer.
Find the probability that a flight departed on time given that it arrives on time.
Birthday Problem You are in a class that has 24 students. You want to find the probability that at least two of the students share the same birthday. (a) First, find the probability that each student has a different birthday. 24 factors P(different birthdays) 365 364 363 362 365 365 365 365 343 342
Reliability of Testing A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 5% of the time if the person does not have the virus. (This 5% result is called a false positive.) Let A be the event "the
P(A) = 0.62, P(A') = 0.38, P(B|A) = 0.41, and P(B|A') = 0.17
P(A) = 0.25, P(A') = 0.75, P(B|A) = 0.3, and P(B|A') = 0.5
P(A) = P(A') = P(B|A) =, and P(B|A') = } ==
and P1B ƒA¿ 2 = 1 P
Birthdays Three people are selected at random. Find the probability that (a) all three share the same birthday and (b) none of the three share the same birthday. Assume 365 days in a year. According to Bayes’ Theorem, the probability of event A, given that event B has occurred, is In Exercises
Warehouses A distribution center receives shipments of a product from three different factories in the following quantities: 50, 35, and 25. Three times a product is selected at random, each time without replacement. Find the probability that (a) all three products came from the third factory and
Bookbinding Defects A printing company’s bookbinding machine has a probability of 0.005 of producing a defective book. This machine is used to bind three books. (a) Find the probability that none of the books are defective. (b) Find the probability that at least one of the books is defective. (c)
Guessing A multiple-choice quiz has five questions, each with four answer choices. Only one of the choices is correct.You have no idea what the answer is to any question and have to guess each answer. (a) Find the probability of answering the first question correctly. (b) Find the probability of
Blood Types The probability that a person in the United States has type blood is 31%. Three unrelated people in the United States are selected at random. (Source: American Association of Blood Banks) (a) Find the probability that all three have type blood. (b) Find the probability that none of the
Blood Types The probability that a person in the United States has type blood is 9%. Five unrelated people in the United States are selected at random. (Source: American Association of Blood Banks) (a) Find the probability that all five have type blood. (b) Find the probability that none of the
Health Care for Dogs The table shows the results of a survey in which 90 dog owners were asked how much they had spent in the last year for their dog’s health care, and whether their dogs were purebred or mixed breeds. (a) Find the probability that $100 or more was spent on a randomly selected
Emergency Savings The table shows the results of a survey in which 142 male and 145 female workers ages 25 to 64 were asked if they had at least one month’s income set aside for emergencies. (a) Find the probability that a randomly selected worker has one month’s income or more set aside for
Batteries Sixteen batteries are tested to see if they last as long as the manufacturer claims. Four batteries fail the test. Two batteries are selected at random without replacement. (a) Find the probability that both batteries fail the test. (b) Find the probability that both batteries pass the
PeopleWho CanWiggleTheir Ears In a sample of 1000 people, 130 can wiggle their ears.Two unrelated people are selected at random without replacement. (a) Find the probability that both people can wiggle their ears. (b) Find the probability that neither person can wiggle his or her ears. (c) Find the
Surviving Surgery A doctor gives a patient a 60% chance of surviving bypass surgery after a heart attack. If the patient survives the surgery, he has a 50% chance that the heart damage will heal. Find the probability that the patient survives surgery and the heart damage heals
Computers and Internet Access A study found that 81% of households in the United States have computers. Of those 81%, 92% have Internet access. Find the probability that a U.S. household selected at random has a computer and has Internet access. (Source: The Nielsen Company)
Government According to a survey, 86% of adults in the United States think the U.S. government system is broken. Of these 86%, about 8 out of 10 think the government can be fixed. (Adapted from CNN/Opinion Research Corporation) (a) Find the probability that a randomly selected adult thinks the U.S.
Assisted Reproductive Technology A study found that 37% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty-five percent of the ART pregnancies resulted in multiple births. (Source: National Center for Chronic Disease Prevention and Health Promotion) (a) Find the
Nursing Majors The table shows the number of male and female students enrolled in nursing at the University of Oklahoma Health Sciences Center for a recent semester. (Source: University of Oklahoma Health Sciences Center Office of Institutional Research) (a) Find the probability that a randomly
Summer Vacation The table shows the results of a survey in which 146 families were asked if they own a computer and if they will be taking a summer vacation during the current year. (a) Find the probability that a randomly selected family is not taking a summer vacation this year. (b) Find the
Pickup Trucks In a survey, 510 adults were asked if they drive a pickup truck and if they drive a Ford. The results showed that one in six adults surveyed drives a pickup truck, and three in ten adults surveyed drive a Ford. Of the adults surveyed that drive Fords, two in nine drive a pickup truck.
BRCA Gene In the general population, one woman in eight will develop breast cancer. Research has shown that approximately 1 woman in 600 carries a mutation of the BRCA gene. About 6 out of 10 women with this mutation develop breast cancer. (Adapted from Susan G. Komen Breast Cancer Foundation) (a)
According to researchers, diabetes is rare in societies in which obesity is rare. In societies in which obesity has been common for at least 20 years, diabetes is also common. (Source: American Diabetes Association)
Studies found that exposure to everyday sources of aluminum does not cause Alzheimer’s disease. (Source: Alzheimer’s Association)
Stress causes the body to produce higher amounts of acid, which can irritate already existing ulcers. But, stress does not cause stomach ulcers. (Source: Baylor College of Medicine)
A study found that people who suffer from moderate to severe sleep apnea are at increased risk of having high blood pressure. (Source: Journal of the American Medical Association)
A ball numbered from 1 through 52 is selected from a bin, replaced, and then a second numbered ball is selected from the bin. Classifying Events Based on Studies In Exercises 13–16, identify the two events described in the study. Do the results indicate that the events are independent or
Rolling a six-sided die and then rolling the die a second time so that the sum of the two rolls is five
Not putting money in a parking meter and getting a parking ticket
A father having hazel eyes and a daughter having hazel eyes
Returning a rented movie after the due date and receiving a late fee
Selecting a king from a standard deck, replacing it, and then selecting a queen from the deck
If events A and B are dependent, then Classifying Events In Exercises 7–12, decide whether the events are independent or dependent. Explain your reasoning.
If two events are independent,
Explain how the complement can be used to find the probability of getting at least one item of a particular type.
What does the notation mean?
List examples of (a) two events that are independent. (b) two events that are dependent.
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