New Semester
Started
Get
50% OFF
Study Help!
--h --m --s
Claim Now
Question Answers
Textbooks
Find textbooks, questions and answers
Oops, something went wrong!
Change your search query and then try again
S
Books
FREE
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Tutors
Online Tutors
Find a Tutor
Hire a Tutor
Become a Tutor
AI Tutor
AI Study Planner
NEW
Sell Books
Search
Search
Sign In
Register
study help
business
bayesian statistics an introduction
Statistics Through Applications 2nd Edition Daren S Starnes, David S Moore, Dan Yates - Solutions
Our dirty little secret More than 90% of people surveyed say they always wash their hands aft er using public restrooms. But observers posted in public restrooms found that only 4679 of 6076 observed individuals actually washed their hands.3(a) What population does inference concern here?(b)
A student survey Tonya wants to estimate what proportion of the seniors in her school plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school. She fi nds that 36 plan to attend the prom.(a) What population does Tonya want to draw conclusions about?(b) What does the
Keno, II Refer to the previous exercise. Suppose a player decides to play 25 games of this simple version of Keno. Let Y 5 the number of games won by the player.(a) Show that this is a binomial setting.(b) Find and interpret P(Y 5 5). Show your work.(c) Find and interpret P(Y . 5). Show your
Keno, I Th e game of Keno is played with 80 balls numbered 1 through 80.During each play of the game, the casino selects 20 of the balls at random. In a simple version of the game, a player pays $1 and chooses one number between 1 and 80. If the player’s number matches one of the 20 randomly
It pays to eat cereal Some time ago, Cheerios cereal boxes displayed a dollar bill on the front of the box and a cartoon character who said, “Free $1 bill in every 20th box.” Mae Lee wants to know how many boxes of Cheerios she can expect to buy in order to get one of the “free” dollar
We like opinion polls Are Americans interested in opinion polls about the major issues of the day? Suppose that 40% of all adults are very interested in such polls. (According to sample surveys that ask this question, 40% is about right.) A polling fi rm chooses an SRS of 1015 people. If they do
Getting a fl ush If you deal fi ve cards from a well-shuffl ed deck, what’s the probability that they’re all the same suit? (Card players call this kind of hand a “fl ush.”)(a) Start by calculating the probability that all fi ve cards are diamonds. Show your work.(b) Now fi nd the
Free throws A basketball player claims to make 80% of her free throws.Suppose this probability is the same for each free throw she attempts. In one game, she shoots 7 free throws. Let X 5 the number of free throws on which she makes a basket.(a) Show that this is a binomial setting.(b) Find the
Phone numbers, II Refer to the previous exercise. Suppose that a computer assigns the seven digits in Nick’s phone number at random, subject to the restriction in Exercise 8.69(b). Find the probability that Nick’s phone number contains no repeated digits. Show your work.
Phone numbers, I In North America, phone numbers have the form XXXXXX-XXXX. Th e fi rst three digits give the area code, and the second three digits indicate the exchange.(a) Nick lives in western North Carolina, where the area code is 828. If there were no restrictions on the remaining seven
What are the chances? Open your local telephone directory to any page in the residential listing. Look at the last four digits of each telephone number, the digits that specify an individual number within an exchange given by the fi rst three digits. Note the fi rst of these four digits in each of
Pastabilities A popular Italian restaurant chain claimed that you could get “42 diff erent pasta-sauce combinations.” Explain what you think they meant by this claim.
Galton’s Board, II Refer to the previous exercise. Let X 5 the number of times that the ball falls to the right.(a) Make a histogram that shows the probability distribution of X. How is this graph diff erent from the one in Figure 8.9 (page 408)?(b) Suppose 100 balls are dropped down the chute,
Galton’s Board, I Refer to Example 8.14 (page 407). A clever person has redesigned the “bean machine” of Figure 8.8. Th e pegs have been adjusted so that a ball is more likely to fall to the right (0.6) than to the left (0.4).(a) Find the probability that a ball lands in Slot A. Show your
Orange M&M’s, II Refer to Exercise 8.63. Let X 5 the number of orange M&M’s chosen.(a) Find the probability distribution of X. Display it in a table.(b) Graph the probability distribution of X. Describe what you see.
Orange M&M’s, I According to the Mars candy company, 20% of its plain M&M’s candies are orange. Assume the company’s claim is true. Suppose you reach into a large bag of plain M&M’s (without looking) and pull out eight candies.(a) Would you be surprised if none of the candies were orange?
Righties and left ies Refer to the previous exercise. Let X 5 the number of right-handed students in your sample.(a) Find and interpret P(X 5 12). How does this compare with your answer to 8.61(a)?(b) Write a probability expression involving X that is equivalent to the question in 8.61(b).(c) Find
More left ies Suppose that exactly 10% of the students at your school are left -handed. Imagine selecting an SRS of 15 students from the school population.(a) Find the probability that exactly 3 students in the sample are left -handed.Show your work.(b) Find the probability that 3 or fewer students
Going to the dogs, II Refer to the previous exercise.(a) What is the expected number of dog owners who greet their dog fi rst when they arrive home? Justify your answer.(b) Make a table that shows the probability distribution of the variable X 5 the number of owners who greet their dog fi rst.(c)
Going to the dogs, I Ladies Home Journal magazine reported that 66% of all dog owners greet their dog before greeting their spouse or children when they return home at the end of the workday. Suppose that 12 dog owners are selected at random.(a) Show that the four requirements for a binomial
Bigger bean machine Draw a Galton’s Board with two more rows of pegs than the one in Figure 8.8. Label the slots at the bottom of the board A through I from left to right.(a) Find the probability that a ball lands in Slot C. Show your work.(b) Find the probability that a ball lands in Slot F.
Coin tosses Imagine that you toss a fair coin six times.(a) Find the probability that you get three heads and three tails. Show your work.(b) Find the probability that you get four heads and two tails. Show your work.
Sowing more seeds Refer to Exercise 8.55.(a) If only 15 seeds actually germinate, should Judy be suspicious that the company’s claim is not true? Compute an appropriate probability to support your answer.(b) If only 12 seeds actually germinate, should Judy be suspicious that the company’s claim
Sowing seeds again Seed Depot advertises that 85% of its fl ower seeds will germinate (grow). Suppose that the company’s claim is true. Judy buys a packet with 20 fl ower seeds from Seed Depot and plants them in her garden.(a) How many seeds should Judy expect to germinate? Explain.(b) Find the
Blood types, II Refer to Exercise 8.53. Let X 5 the number of people chosen with type O blood.(a) Find the probability distribution of X. Display it in a table.(b) Graph the probability distribution of X. Describe what you see.
Blood types, I In the United States, 44% of adults have type O blood.Suppose we choose seven U.S. adults at random.(a) What’s the probability that all seven people have type O blood? Show your method.(b) What’s the probability that exactly four of those selected have type O blood?Show your
Th ree winners Refer to Example 8.13 (page 402). Find the probability that exactly three of the six friends win a prize. Show your work.
All 6 win Refer to Example 8.13 (page 402). Find the probability that Alan and all fi ve of his friends win a prize. Show your work.
Left ies, II About 10% of people are left -handed. Select 15 students at random from your school and count the number who are left -handed.
Left ies, I About 10% of people are left -handed. Suppose you select students at random from your school, one at a time, until you fi nd one who is left -handed.Record the number of students you selected.
Long or short? Put the names of all the students in your class in a hat.Mix them up, and draw four names without looking. Count the number of these students whose last names have more than six letters.
Sowing seeds Seed Depot advertises that 85% of its fl ower seeds will germinate (grow). Suppose that the company’s claim is true. Judy buys a packet with 20 fl ower seeds from Seed Depot and plants them in her garden. She counts how many of the seeds germinate.
Deal or No Deal? In Activity 8.2 (page 387), you explored the TV game show Deal or No Deal. Now, you should be ready to analyze some of the probabilities involved in the game. Suppose you get very lucky and choose the case with$1 million in it as your case. In the fi rst round of the game, you must
Roll 5 dice Suppose you roll 5 six-sided dice at one time.(a) Find the probability that all 5 dice show the same number of spots on the upfaces.Show your work.(b) What’s the probability that all 5 dice show a diff erent number of spots on the up-faces? Show your work.
Pick Six again Refer to Exercise 8.43. Find the probability that an unlucky player does not match any of the six winning numbers. Show your work.
Pick Six In the New Jersey “Pick Six” lotto game, a player chooses six diff erent numbers from 1 to 49. Th e six winning numbers for the lottery are chosen at random.If the player matches all six numbers, she wins the jackpot, which starts at $2 million. Find the probability of picking all six
Who else gets picked? Refer to Exercise 8.41. Th is time, Mr. Paradise uses his program three times in a row. Find the probability that three diff erent students in the class are chosen.
Who gets picked? Mr. Paradise uses a calculator program to select students at random to answer questions during class. Each of the 28 students in his class is equally likely to be chosen every time he runs the program. Suppose Mr. Paradise runs the program twice. Th e fi rst student selected gets
Radio station call signs, II Refer to Exercise 8.39. By 1922, there were more applications for radio station licenses than the number of three-letter call signs available.A radio station in New Orleans applied for and was granted the call sign WAAB.(a) How many four-letter call signs start with the
Radio station call signs, I In 1912, the U.S. government began issuing licenses to radio stations. Each station was given a unique three-letter “call sign.” By international agreement, the U.S. eventually received rights to all call signs beginning with the letters W, N, and K. Radio stations
Big slick In Texas Hold ’Em, players are initially dealt two cards. One very strong starting hand is called “big slick,” which consists of an ace and a king (not necessarily of the same suit).(a) If you deal two cards from a well-shuffl ed deck, what’s the probability of getting “big
Permutations and combinations Six friends—Aaron, Betty, Caleb, Deanne, Ernie, and Flo—are having a study session on permutations and combinations.(a) Find the value of 6P0. Explain why this value makes sense.(b) Compute the value of 6P3 and 6C3. Create an example involving the six friends to
Pick 4 Refer to Example 8.10. In the Pick 4 game of the Tri-State Daily Numbers, you pay $1 and choose a four-digit number. Th e state chooses a fourdigit winning number at random and pays you $5000 if your number is chosen.(a) What’s the probability that you win? Show your method clearly.(b)
Pick 3 more Refer to Example 8.10.(a) Find the number of ways in which the computer can pick a winning number with three diff erent digits. Show your work.(b) What’s the probability that the computer picks a winning number with two or more matching digits? Show your work.
Th ree scoops Refer to Exercise 8.33. How many diff erent ways are there to order(a) a cone with three scoops if you care about the order of fl avors?(b) a cone with three scoops of diff erent fl avors if you care about the order of fl avors?(c) a cup with three scoops of diff erent fl avors (order
Two scoops On the way home, you decide to stop by 28 Choices ice cream parlor for a snack. With 28 fl avors to choose from, how many diff erent ways are there to order:(a) a cone with two scoops if you care about the order of fl avors?(b) a cone with two scoops of diff erent fl avors if you care
Assigned seating Mrs. Random decides to randomly assign seats for the 25 students in her statistics class.(a) If there are 25 seats in the classroom, how many diff erent seating assignments are possible? Show your work.(b) Repeat part (a) for a classroom with 30 seats.
Organizing homework Suppose you have six homework assignments to complete one night.(a) In how many diff erent orders can you complete all of the assignments?(b) In how many diff erent orders can you complete all six assignments if you simply must do your statistics assignment fi rst?
New Jersey plates, II Refer to the previous exercise. In 1999, New Jersey license plates were actually not allowed to have the letters D, T, or X in the fi rst position, or the letters I, O, or Q in any position. With these restrictions, how many diff erent license plates were actually possible in
New Jersey plates, I Th e illustration shows what New Jersey license plates looked like in two diff erent years—1959 and 1999. Assume that letters and numbers must be in the positions shown on each license plate: for 1959, three letters followed by three numbers; for 1999, three letters, then two
More ice cream Refer to Example 8.8. Mary stops by 28 Choices on the way home from school. She only has enough money for a sundae with one scoop of ice cream and one topping in a small bowl. How many diff erent choices does Mary have for her sundae?
More domain names Refer to Example 8.7. How many three-character Internet domain names are possible that consist of(a) letters only?(b) numbers or letters?Note: All three-character domain names have been taken.
Collecting cereal box prizes Several years ago, every box of Frosted Mini-Wheats contained a NASCAR driver’s decal. Th ere was a set of 6 decals, and consumers were encouraged to “collect all 6.” Th e probability model is Every box of Frosted Mini-Wheats cereal contains one NASCAR driver’s
Polling women, II In the setting of Exercise 8.24, what is the probability of getting a sample in which more than 51% of the women think they do not get enough time for themselves? Show your work. (Use Table A or your calculator.)
Polling women, I Suppose that 47% of all adult women think they do not get enough time for themselves. An opinion poll interviews 1025 randomly chosen women and records the sample proportion who feel they don’t get enough time for themselves. Th is statistic will vary from sample to sample if the
Fire insurance Suppose a homeowner spends $300 for a home insurance policy that will pay out $200,000 if the home is destroyed by fi re. Let Y 5 the profi t made by the insurance company on a single policy. From previous data, the probability that a home in this area will be destroyed by fi re is
Pop a balloon, IV Make a new table of prices and numbers of slips so that the expected price a customer will pay in the pop-the-balloon game is 40 cents.Use a total of 100 slips.
Pop a balloon, III Compute the expected price of an ice cream bar when Mary pops a balloon. Is it to her benefi t to play the raffl e? Explain.
Pop a balloon, II Sketch a graph of the probability distribution of X.
Pop a balloon, I(a) Find P(X , $0.10) and interpret your result.(b) What is the probability that Mary will pay less than the usual cost of an ice cream bar? Write this probability in terms of the random variable X.(c) How much money will the store take in if all of the balloons are popped? How much
An IQ test, III How high must a person score on the WAIS test to be in the top 10% of all scores? Use Table A or your calculator to answer this question.Show your work.Exercises 8.16 to 8.18 refer to the following setting. Th e Wechsler Adult Intelligence Scale (WAIS) is a common “IQ test” for
An IQ test, II Use Table A or your calculator to fi nd the probability that a randomly chosen person has a WAIS score of 112 or higher. Show your work.Exercises 8.16 to 8.18 refer to the following setting. Th e Wechsler Adult Intelligence Scale (WAIS) is a common “IQ test” for adults. Th e
An IQ test, I(a) What is the probability that a randomly chosen individual has a WAIS score of 115 or higher?(b) In what range do the scores of the middle 95% of the adult population lie?Exercises 8.16 to 8.18 refer to the following setting. Th e Wechsler Adult Intelligence Scale (WAIS) is a common
Generating a sampling distribution Let us illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. Th e population consists of the numbers 1, 2, 4, and 9. Th e parameter of interest is the mean of this population. Th e sample is an SRS of size
Applying to college You ask an SRS of 1500 college students whether they applied for admission to any other college. Suppose that in fact 75% of all college students applied to colleges besides the one they are attending. (Th at’s close to the truth.) Th e sampling distribution of the proportion
Do you jog? An opinion poll asks an SRS of 1500 adults, “Do you happen to jog?” Suppose (as is approximately correct) that the population proportion who jog is p 5 0.15. In a large number of samples, the proportion p^ who answer “Yes”will be approximately Normally distributed with mean 0.15
Birthdays revisited Refer to the previous exercise. On average, how many diff erent people can you expect to ask before you fi nd two with the same birthday? Use Table B or your calculator to simulate birthdays of randomly chosen people until you hit the same birthday a second time.(a) How many
Duplicate birthdays There are 30 students in Austin’s precalculus class, all unrelated. He wants to bet you $1 that at least 2 of the students were born on the same day of the year (same month and day but not necessarily the same year). Should you take the bet? Before you answer, you decide to
Bringing down the house? You may have heard about a group of MIT students who beat the casinos at blackjack. Th e 2008 movie 21 and the book Bringing Down the House tell their story. Do some research: how did the students use probability to get an edge on the casinos?
Selecting a jury A county selects people for jury duty at random from a list of one million registered voters, which happens to be evenly divided in terms of gender (that is, exactly 50% of the county’s registered voters are women). Which of the following is true and which is false? Explain.(a)
Spin the wheel Joey has been watching people play roulette for a few minutes. In the past 20 spins of the wheel, the ball has landed in a red slot 14 times. Joey wants to place a bet on “black” for the next spin, because he believes black is “due.” He asks you for advice. What do you tell
16 boys! Th e Associated Press reported an unusual occurrence at the Canton-Potsdam Hospital in Potsdam, New York: between December 15 and December 21, all 16 newborns at the hospital were boys.(a) Would the births of 16 consecutive boys at a diff erent hospital in another small town in the United
Roll two dice, II Refer to Exercise 8.2. Find the expected value of T and interpret the result.
Random digits, II Refer to Exercise 8.1. Find the expected value of D and interpret the result.
Household size According to the Census Bureau, the number of people X in a randomly selected U.S. household follows the probability distribution given in the table below.(a) Sketch a histogram that displays the probability distribution of X.(b) Calculate and interpret P(X . 2).(c) Find the expected
Unhealthy babies Refer to Example 8.1. Newborns with Apgar scores of 3 and below may require medical attention. Write the probability that a randomly chosen baby has an Apgar score of 3 or below in terms of the random variable Y.Th en fi nd this probability.
Roll two dice, I Imagine that you roll two fair, six-sided dice—one red and one green. Let T 5 the sum of the spots showing on the up-faces of the two dice.(a) Explain why T is a random variable.(b) Display the probability distribution of T in a table.(c) Construct a histogram that shows the
Random digits, I Imagine choosing a digit from 0 to 9 at random, either from Table B or with your calculator. Let D 5 the digit selected.(a) Explain why D is a random variable.(b) Display the probability distribution of D in a table.(c) Construct a histogram that shows the probability distribution
Drug use in baseball On December 13, 2007, former senator George Mitchell released an extensive report on the use of performance-enhancing drugs in Major League Baseball. He even included a list of players who had been using such drugs.One question of interest is whether performance-enhancing drugs
Random digits Suppose you instruct your calculator to choose a random digit from 0 to 9. Defi ne two events A and B related to this chance process that are mutually exclusive but not complements of each other.
Looking for metal A boy uses a homemade metal detector to look for valuable metal objects on a beach. Th e machine isn’t perfect—it identifi es only 98% of the metal objects over which it passes, and it identifi es 4% of the nonmetallic objects over which it passes. Suppose that 25% of the
Challenger disaster On January 28, 1986, Space Shuttle Challenger exploded on takeoff . All seven crew members were killed. Following the disaster, scientists and statisticians helped analyze what went wrong. Th ey determined that the failure of o-ring joints in the shuttle’s booster rockets was
More smokers Draw a Venn diagram to represent the sample space of Exercise 7.83.
Who smokes? Th e question “Do you smoke?” was asked of a random sample of 100 people. Results are shown in the table below. Suppose we select one of these people at random.(a) What’s the probability that the person smokes?(b) Given that the person is male, what’s the probability that the
Th e girls Suppose that about 48% of all infants are girls. Th e maternity ward of a large hospital handles 1000 deliveries per year. A smaller hospital in the same city records about 50 deliveries per year. At which hospital is it more likely that between 46% and 50% of the babies born there this
Class rank Choose a college student at random and ask his or her class rank in high school. Probabilities for the outcomes are(a) What must be the probability that a randomly chosen student was in the bottom half of his or her high school class?(b) To simulate the class standing of randomly chosen
Sandblasters 2007 Eight teams of the world’s best sand sculptors gathered near San Diego, California, for Sandblasters 2007: Th e Extreme Sand Sculpting Competition. At fi ve points during the competition, a randomly selected team’s sculpture was blown up.Th at team was then forced to build a
A dice game Your teacher has invented another “fair” dice game to play. Here’s how it works. Your teacher will roll one fair eight-sided die, and you will roll a fair sixsided die. Each player rolls once, and the winner is the person with a higher number.In case of a tie, neither player
Activity 7.3 follow-up Return to Activity 7.3 (page 348). Assume that your teacher has probability 2/3 of winning any individual round.(a) List the sample space for the weird dice game. Find the probability for each possible outcome.(b) Find the probability that the teacher wins the next game. Show
Th e birthday problem If 30 unrelated people are in a room at the same time, what’s the probability that at least 2 of them have the same birthday (month and day)? Make a guess before you perform any calculations.(a) Let’s start with a simpler problem. If 2 unrelated people are in a room,
Testing the test Are false positives too common in some medical tests?Researchers conducted an experiment involving 250 patients with a medical condition and 750 other patients who did not have the medical condition. The medical technicians who were reading the test results were unaware that they
Cats and dogs In an elementary school classroom, there are 40 students.For every student, we record whether they have a cat and whether they have a dog.Thirty students say that they have a dog, and 20 students say that they have a cat.If possible, make a two-way table in which the events D has a
Th e chevalier’s other problem To increase interest among French gamblers, another game was devised in which players bet on getting at least 1 set of “double 1s” when rolling a pair of fair, six-sided dice 24 times. The chevalier de Mere, a frequent gambler, believed that the probability of
Th e chevalier’s problem In the early 1700s, French gamblers played a game in which they bet on getting at least one “1” when a fair, six-sided die was rolled four times.(a) Draw a tree diagram that shows the sample space of this chance process.(b) Find the probability of interest. Show your
TCNJ survey, III Exercise 7.46 (page 347) described the results of a class survey. Here is the two-way table that shows the gender and handedness of the students in the class:(a) What percent of the males in the class are right-handed?(b) What percent of the right-handed people in the class are
Tall people and basketball players Select an adult at random. Let T 5 person is over 6 feet tall and B 5 person is a professional basketball player. Rank the following probabilities from smallest to largest. Justify your answer.P(T) P(B) P(T|B) P(B|T)
Testing for AIDS, II Refer to the previous exercise. Suppose that we use the ELISA test in an area where only 0.1% of the population has HIV. Repeat parts(a), (b), and (c). Are you surprised?
Testing for AIDS, I The ELISA test can help detect whether people have the AIDS virus (HIV). As with any medical test, ELISA can give false positive and false negative results. From experience, medical researchers estimate that the ELISA test has a 0.2% false positive rate and a 0.1% false negative
False positives and negatives Which is a more serious error in each of the following situations—a false positive result or a false negative result? Justify your answer.(a) Testing athletes for performance-enhancing drugs.(b) Testing people for a life-threatening disease.
Assessing risk Refer to Example 7.25 (page 358). Use the probabilities provided to make a table that shows the status of 1000 randomly selected patients with Morris’s condition.
Showing 1100 - 1200
of 2867
First
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Last
Step by Step Answers
Get 50% OFF
Claim Now
