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

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
business
business statistics communicating

Introduction To The Practice Of Statistics 6th Edition David S. Moore, George P. McCabe, Bruce A. Craig - Solutions

Find the mean and the standard deviation of the sampling distribution.You take an SRS of size 25 from a population with mean 200 and standard deviation 10. Find the mean and standard deviation of the sampling distribution of your sample mean.
CHALLENGE The geometric distribution. Generalize your work in Exercise 5.34. You have independent trials, each resulting in a success or a failure. The probability of a success is p on each trial. The binomial distribution describes the count of successes in a fixed number of trials. Now the number
Tossing a die. You are tossing a balanced die that has probability 1/6 of coming up 1 on each toss.Tosses are independent. We are interested in how long we must wait to get the first 1.(a) The probability of a 1 on the first toss is 1/6.What is the probability that the first toss is not a 1 and the
Multiple-choice tests. Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of an
CHALLEN GE Show that these facts are true. Use the definition of binomial coefficients to show that each of the following facts is true. Then restate each fact in words in terms of the number of ways that k successes can be distributed among n observations.(a)n n= 1 for any whole number n ≥
Checking for problems with a sample survey.One way of checking the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known demographic facts about the population. The 2000 census found that 23,772,494 of the 209,128,094 adults (aged 18
CHALLENGE Scuba-diving trips. The mailing list of an agency that markets scuba-diving trips to the Florida Keys contains 60% males and 40% females.The agency calls 30 people chosen at random from its list.(a) What is the probability that 20 of the 30 are men? (Use the binomial probability
CHALLENGE Is the ESP result better than guessing?When the ESP study of Exercise 5.27 discovers a subject whose performance appears to be better than guessing, the study continues at greater length. The experimenter looks at many cards bearing one of five shapes (star, square, circle, wave, and
Admitting students to college. A selective college would like to have an entering class of 950 students.Because not all students who are offered admission accept, the college admits more than 950 students.Past experience shows that about 75% of the students admitted will accept. The college decides
A test for ESP. In a test for ESP (extrasensory perception), the experimenter looks at cards that are hidden from the subject. Each card contains either a star, a circle, a wave, or a square. As the experimenter looks at each of 20 cards in turn, the subject names the shape on the card.(a) If a
CHALLENGE How large a sample is needed? The changing probabilities you found in Exercises 5.22 and 5.24 are due to the fact that the standard deviation of the sample proportionˆp gets smaller as the sample size n increases. If the population proportion is p = 0.49, how large a sample is needed to
CHALLEN GE A college alcohol study. The Harvard College Alcohol Study finds that 67% of college students support efforts to “crack down on underage drinking.” The study took a sample of almost 15,000 students, so the population proportion who support a crackdown is very close to p = 0.67.5 The
How do the results depend on the sample size?Return to the Gallup Poll setting of Exercise 5.22.We are supposing that the proportion of all adults who think that two children is ideal is p = 0.49.What is the probability that a sample proportionˆp falls between 0.46 and 0.52 (that is, within ±3
Visiting a casino and betting on college sports. A Gallup Poll finds that 30% of adults visited a casino in the past 12 months, and that 6% bet on college sports.4 These results come from a random sample of 1011 adults. For an SRS of size n = 1011:(a) What is the probability that the sample
The ideal number of children. “What do you think is the ideal number of children for a family to have?” A Gallup Poll asked this question of 1016 randomly chosen adults. Almost half (49%) thought two children was ideal.3 Suppose that p = 0.49 is exactly true for the population of all adults.
Inheritance of blood types. Children inherit their blood type from their parents, with probabilities that reflect the parents’ genetic makeup. Children of Juan and Maria each have probability 1/4 of having blood type A and inherit independently of each other. Juan and Maria plan to have 4
APPLET Use the Probability applet. The Probability applet simulates tosses of a coin. You can choose the number of tosses n and the probability p of a head. You can therefore use the applet to simulate binomial random variables.The count of misclassified sales records in Example 5.8 (page 317) has
Random digits. Each entry in a table of random digits like Table B has probability 0.1 of being a 0, and digits are independent of each other.(a) What is the probability that a group of five digits from the table will contain at least one 5?(b) What is the mean number of 5s in lines 40 digits long?
Attitudes toward drinking and behavior studies. Some of the methods in this section are approximations rather than exact probability results. We have given rules of thumb for safe use of these approximations.(a) You are interested in attitudes toward drinking among the 75 members of a fraternity.
CHALLENGE Typographic errors. In the proofreading setting of Exercise 5.13, what is the smallest number of misses m with P(X ≥ m) no larger than 0.05? You might consider m or more misses as evidence that a proofreader actually catches fewer than 70% of word errors.
Visits to Web sites. Suppose that 50% of male Internet users aged 18 to 34 have visited an auction site at least once in the past month.(a) If you interview 15 at random, what is the mean of the count X who have visited an auction site?What is the mean of the proportion ˆp in your sample who have
Typographic errors. Return to the proofreading setting of Exercise 5.13.(a) What is the mean number of errors caught?What is the mean number of errors missed? You see that these two means must add to 10, the total number of errors.(b) What is the standard deviation σ of the number of errors
Visits to Web sites.What kinds of Web sites do males aged 18 to 34 visit most often? Pornographic sites take first place, but about 50% of male Internet users in this age group visit an auction site such as eBay at least once a month.2 Interview a random sample of 15 male Internet users aged 18 to
Typographic errors. Typographic errors in a text are either nonword errors (as when “the” is typed as “teh”) or word errors that result in a real but incorrect word. Spell-checking software will catch nonword errors but not word errors. Human proofreaders catch 70% of word errors. You ask a
Should you use the binomial distribution? In each situation below, is it reasonable to use a binomial distribution for the random variable X?Give reasons for your answer in each case.(a) A random sample of students in a fitness study.X is the mean systolic blood pressure of the sample.(b) A
Should you use the binomial distribution? In each situation below, is it reasonable to use a binomial distribution for the random variable X?Give reasons for your answer in each case. If a binomial distribution applies, give the values of n and p.(a) A poll of 200 college students asks whether or
What is wrong? Explain what is wrong in each of the following scenarios.(a) In the binomial setting X is a proportion.(b) The variance for a binomial count is p(1 − p)/n.(c) The Normal approximation to the binomial distribution is always accurate when n is greater than 1000.
What is wrong? Explain what is wrong in each of the following scenarios.(a) If you toss a fair coin three times and a head appears each time, then the next toss is more likely to be a tail than a head.(b) If you toss a fair coin three times and a head appears each time, then the next toss is more
A bent coin. A coin is slightly bent, and as a result the probability of a head is 0.52. Suppose that you toss the coin four times.(a) Use the binomial formula to find the probability of 3 or more heads.(b) Compare your answer with the one that you would obtain if the coin were fair.
Use the Normal approximation. Suppose we toss a fair coin 100 times. Use the Normal approximation to find the probability that the sample proportion is(a) between 0.4 and 0.6. (b) between 0.45 and 0.55.
Find the mean and the standard deviation. If we toss a fair coin 100 times, the number of heads is a random variable that is binomial.(a) Find the mean and the standard deviation of the sample proportion.(b) Is your answer to part (a) the same as the mean and the standard deviation of the sample
Find the probabilities.(a) Suppose X has the B(4, 0.3) distribution. Use software or Table C to find P(X = 0) and P(X ≥ 3).(b) Suppose X has the B(4, 0.7) distribution. Use software or Table C to find P(X = 4) and P(X ≤ 1).(c) Explain the relationship between your answers to parts (a) and (b)of
Genetics and blood types. Genetics says that children receive genes from their parents independently. Suppose each child of a particular pair of parents has probability 0.25 of having type O blood. If these parents have 4 children, what is the distribution of the number who have type O blood?
Toss a coin. Toss a fair coin 20 times. Give the distribution of X, and the number of heads that you observe.
Seniors who have taken a statistics course. In a random sample of 200 senior students from your college, 40% reported that they had taken a statistics course. Give n, X, and ˆp for this setting.
Use of the Internet to find a place to live. A poll of 1500 college students asked whether or not they had used the Internet to find a place to live sometime within the past year. There were 525 students who answered “Yes”; the other 975 answered “No.”(a) What is n?(b) Choose one of the two
Suppose that in fact the probability is 0.3 that a randomly chosen student has plagiarized a paper. Draw a tree diagram in which the first stage is tossing the coin and the second is the truth about plagiarism. The outcome at the end of each branch is the answer given to the randomizedresponse
CH ALLENGE Sample surveys for sensitive issues. It is difficult to conduct sample surveys on sensitive issues because many people will not answer questions if the answers might embarrass them. Randomized response is an effective way to guarantee anonymity while collecting information on topics such
Find some conditional probabilities. Choose a point at random in the square with sides 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. This means that the probability that the point falls in any region within the square is the area of that region. Let X be the x coordinate and Y the y coordinate of the point
An interesting case of independence.Independence of events is not always obvious.Toss two balanced coins independently. The four possible combinations of heads and tails in order each have probability 0.25. The events A = head on the first toss B = both tosses have the same outcome may seem
Internet usage patterns of students and other adults. Students have different patterns of Internet use than other adults. Among adult Internet users, 4.1% are full-time students and another 2.9% are part-time students. Students are much more likely to access the Internet from someplace other than
Wine tasting. In the setting of Exercise 4.135, Taster 1’s rating for a wine is 3. What is the conditional probability that Taster 2’s rating is higher than 3?
Weights and heights of children adjusted for age. The idea of conditional probabilities has many interesting applications, including the idea of a conditional distribution. For example, the National Center for Health Statistics produces distributions for weight and height for children while
Odds bets at craps. Refer to the odds bets at craps in Exercise 4.133. Suppose that whenever the shooter has an initial roll of 4, 5, 6, 8, 9, or 10, you take the odds. Here are the probabilities for these initial rolls:Point 4 5 6 8 9 10 Probability 3/36 4/36 5/36 5/36 4/36 3/36 Draw a tree
Higher education at 2-year and 4-year institutions.The following table gives the counts of U.S. institutions of higher education classified as public or private and as 2-year or 4-year:31 Public Private 2-year 639 1894 4-year 1061 622 Convert the counts to probabilities and summarize the
CHALLENGE Slot machines. Slot machines are now video games, with winning determined by electronic random number generators. In the old days, slot machines were like this: you pull the lever to spin three wheels; each wheel has 20 symbols, all equally likely to show when the wheel stops spinning;
CHALL ENGE Lottery tickets. Joe buys a ticket in the TriState Pick 3 lottery every day, always betting on 956. He will win something if the winning number contains 9, 5, and 6 in any order.Each day, Joe has probability 0.006 of winning, and he wins (or not) independently of other days because a new
CHALL ENGE SAT scores. The College Board finds that the distribution of students’ SAT scores depends on the level of education their parents have. Children of parents who did not finish high school have SAT Math scores X with mean 445 and standard deviation 106. Scores Y of children of parents
Prizes for grocery store customers. A grocery store gives its customers cards that may win them a prize when matched with other cards. The back of the card announces the following probabilities of winning various amounts if a customer visits the store 10 times:Amount $1000 $250 $100 $10 Probability
Profits from an investment. Rotter Partners is planning amajor investment. The amount of profit X is uncertain but a probabilistic estimate gives the following distribution (in millions of dollars):Profit 1 1.5 2 4 10 Probability 0.4 0.2 0.2 0.1 0.1(a) Find the mean profit μX and the standard
Wine tasters. Two wine tasters rate each wine they taste on a scale of 1 to 5. From data on their ratings of a large number of wines, we obtain the following probabilities for both tasters’ ratings of a randomly chosen wine:Taster 2 Taster 1 1 2 3 4 5 1 0.03 0.02 0.01 0.00 0.00 2 0.02 0.07 0.06
An ancient Korean drinking game. An ancient Korean drinking game involves a 14-sided die.The players roll the die in turn and must submit to whatever humiliation is written on the up-face:something like “Keep still when tickled on face.”Six of the 14 faces are squares. Let’s call them A, B,
A fair bet at craps. Almost all bets made at gambling casinos favor the house. In other words, the difference between the amount bet and the mean of the distribution of the payoff is a positive number. An exception is “taking the odds” at the game of craps, a bet that a player can make under
Some probability distributions. Here is a probability distribution for a random variable X:Value of X 1 2 3 Probability 0.2 0.6 0.2(a) Find the mean and standard deviation for this distribution.(b) Construct a different probability distribution with the same possible values, the same mean, and a
Find the probabilities. Refer to the previous exercise. Find the probabilities for each event.
Toss a pair of dice two times. Consider tossing a pair of fair dice two times. For each of the following pairs of events, tell whether they are disjoint, independent, or neither.(a) A = 7 on the first roll, B = 6 or less on the first roll.(b) A = 7 on the first roll, B = 6 or less on the second
Muscular dystrophy. Muscular dystrophy is an incurable muscle-wasting disease. The most common and serious type, called DMD, is caused by a sex-linked recessive mutation. Specifically:women can be carriers but do not get the disease; a son of a carrier has probability 0.5 of having DMD;a daughter
Use Bayes’s rule. Refer to the previous exercise.Jason knows that he is a carrier of cystic fibrosis.His wife, Julianne, has a brother with cystic fibrosis, which means the probability is 2/3 that she is a carrier. If Julianne is a carrier, each child she has with Jason has probability 1/4 of
Cystic fibrosis. Cystic fibrosis is a lung disorder that often results in death. It is inherited but can be inherited only if both parents are carriers of an abnormal gene. In 1989, the CF gene that is abnormal in carriers of cystic fibrosis was identified. The probability that a randomly chosen
Find some conditional probabilities. Beth knows the probabilities for her genetic types from part (c)of the previous exercise. She marries Bob, who is albino. Bob’s genetic type must be aa.(a) What is the conditional probability that a child of Beth and Bob is non-albino if Beth has type Aa?What
Albinism. People with albinism have little pigment in their skin, hair, and eyes. The gene that governs albinism has two forms (called alleles), which we denote by a and A. Each person has a pair of these genes, one inherited from each parent.A child inherits one of each parent’s two alleles,
CHALL ENGE Mathematics degrees and gender. Of the 16,071 degrees in mathematics given by U.S. colleges and universities in a recent year, 73% were bachelor’s degrees, 21% were master’s degrees, and the rest were doctorates. Moreover, women earned 48% of the bachelor’s degrees, 42%of the
Spelling errors. As explained in Exercise 4.74(page 286), spelling errors in a text can be either nonword errors or word errors. Nonword errors make up 25% of all errors. A human proofreader will catch 90% of nonword errors and 70% of word errors. What percent of all errors will the proofreader
CH ALLENG E Gender and majors. The probability that a randomly chosen student at the University of New Harmony is a woman is 0.62. The probability that the student is studying education is 0.17. The conditional probability that the student is a woman, given that the student is studying education,
CH ALLENGE A lurking variable. Beware the lurking variable. The low labor force participation rate of people who did not finish high school is explained by the confounding of education level with a variable that lurks behind the “aged 25 years and over” restriction for these data. Explain this
Find some conditional probabilities. You know that a person is employed. What is the conditional probability that he or she is a college graduate? You know that a second person is a college graduate.What is the conditional probability that he or she is employed?
Conditional probabilities and independence.(a) What is the probability that a randomly chosen person 25 years of age or older is in the labor force?(b) If you know that the person chosen is a college graduate, what is the conditional probability that he or she is in the labor force?(c) Are the
Find the unemployment rates. Find the unemployment rate for people with each level of education. How does the unemployment rate change with education? Explain carefully why your results show that level of education and being employed are not independent.
Find some probabilities. The previous exercise gives the projected number (in thousands) of earned degrees in the United States in the 2010–2011 academic year. Use these data to answer the following questions.(a) What is the probability that a randomly chosen degree recipient is a man?(b) What is
Academic degrees and gender. Here are the projected numbers (in thousands) of earned degrees in the United States in the 2010–2011 academic year, classified by level and by the sex of the degree recipient:28 Bachelor’s Master’s Professional Doctorate Female 933 402 51 26 Male 661 260 44 26(a)
Find a conditional probability. If Julie is offered the federal job, what is the conditional probability that she is also offered the New Jersey job? If Julie is offered the New Jersey job, what is the conditional probability that she is also offered the federal job?
Find the probability of another event. What is the probability that Julie is offered both the Connecticut and New Jersey jobs, but not the federal job?
Find the probability of at least one offer. What is the probability that Julie is offered at least one of the three jobs?
Job offers. Julie is graduating from college. She has studied biology, chemistry, and computing and hopes to work as a forensic scientist applying her science background to crime investigation.Late one night she thinks about some jobs she has applied for. Let A, B, and C be the events that Julie is
Conditional probabilities and independence.Using the information in Exercise 4.109, answer these questions.(a) Given that a vehicle is imported, what is the conditional probability that it is a light truck?(b) Are the events “vehicle is a light truck” and“vehicle is imported” independent?
Income tax returns. In 2004, the Internal Revenue Service received 312,226,042 individual tax returns.Of these, 12,757,005 reported an adjusted gross income of at least $100,000, and 240,128 reported at least $1 million.27 If you know that a randomly chosen return shows an income of $100,000 or
Sales of cars and light trucks. Motor vehicles sold to individuals are classified as either cars or light trucks (including SUVs) and as either domestic or imported. In a recent year, 69% of vehicles sold were light trucks, 78% were domestic, and 55%were domestic light trucks. Let A be the event
Draw a Venn diagram. Draw a Venn diagram that shows the relation between the events A and B in Exercise 4.106. Indicate each of the following events on your diagram and use the information in Exercise 4.106 to calculate the probability of each event. Finally, describe in words what each event
Find a conditional probability. In the setting of the previous exercise, what is the conditional probability that a household is prosperous, given that it is educated? Explain why your result shows that events A and B are not independent.
Education and income. Call a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated.According
Draw a different tree diagram for the same setting. Refer to the previous two exercises. Draw a tree diagram to illustrate the probabilities in a situation where you first identify the gender of the student and then identify the type of institution attended. Explain why the probabilities in this
Draw a tree diagram. Refer to the previous exercise. Draw a tree diagram to illustrate the probabilities in a situation where you first identify the type of institution attended and then identify the gender of the student.
Attendance at 2-year and 4-year colleges. In a large national population of college students, 61%attend 4-year institutions and the rest attend 2-year institutions. Males make up 44% of the students in the 4-year institutions and 41% of the students in the 2-year institutions.(a) Find the four
Find some probabilities. Refer to the previous exercise.(a) Find the probability that a randomly selected student is a male binge drinker, and find the probability that a randomly selected student is a female binge drinker.(b) Find the probability that a student is a binge drinker, given that the
Binge drinking and gender. In a college population, students are classified by gender and whether or not they are frequent binge drinkers.Here are the probabilities:Men Women Binge drinker 0.11 0.12 Not binge drinker 0.32 0.45(a) Verify that the sum of the probabilities is 1.(b) What is the
Draw a tree diagram. Refer to Slim’s chances of a flush in Exercise 4.98. Draw a tree diagram to describe the outcomes for the two cards that he will be dealt. At the first stage, his draw can be a diamond or a non-diamond. At the second stage, he has the same possible outcomes but the
Find the conditional probability. Refer to Table 4.1. What is the conditional probability that a grade is a B, given that it comes from Engineering and Physical Sciences? Find the answer by dividing two numbers from Table 4.1 and using the multiplication rule according to the method in Example 4.45.
The probability that the next two cards are diamonds. In the setting of Exercise 4.44, suppose Slim sees 25 cards and the only diamonds are the 3 in his hand. What is the probability that the next 2 cards dealt to Slim will be diamonds? This outcome would give him 5 cards from the same suit, a hand
Select a grade from the population. Refer to Table 4.1 and consider selecting a single grade from this population.(a) What is the probability that the grade is from Health and Human Services?(b) What is the probability that the grade is an A?(c) What is the probability that the grade is an A, given
The probability of another ace. Suppose two of the four cards in Slim’s hand are aces. What is the probability that the next card dealt to him is an ace?
Probability that your roll is even or greater than 4. If you roll a die, the probability of each of the six possible outcomes (1, 2, 3, 4, 5, 6) is 1/6. What is the probability that your roll is even or greater than 4?
Probability that you roll a 3 or a 5. If you roll a die, the probability of each of the six possible outcomes (1, 2, 3, 4, 5, 6) is 1/6. What is the probability that you roll a 3 or a 5?
A portfolio with three investments. Portfolios often contain more than two investments. The rules for means and variances continue to apply, though the arithmetic gets messier. A portfolio containing proportions a of 500 Index Fund, b of Investment Grade Bond Fund, and c of Diversified
The effect of correlation. Diversification works better when the investments in a portfolio have small correlations. To demonstrate this, suppose that returns on 500 Index Fund and Diversified International Fund had the means and standard deviations we have given but were uncorrelated(ρWY = 0).
Investing in a mix of U.S. stocks and foreign stocks. Many advisers recommend using roughly 20% foreign stocks to diversify portfolios of U.S.stocks. You see that the 500 Index (U.S. stocks) and Diversified International (foreign stocks) Funds had almost the same mean returns. A portfolio of 80%500
Risk for one versus thousands of life insurance policies. It would be quite risky for you to insure the life of a 25-year-old friend under the terms of Exercise 4.89. There is a high probability that your friend would live and you would gain $875 in premiums. But if he were to die, you would lose
Life insurance. According to the current Commissioners’ Standard Ordinary mortality table, adopted by state insurance regulators in December 2002, a 25-year-old man has these probabilities of dying during the next five years:21 Age at death 25 26 27 28 29 Probability 0.00039 0.00044 0.00051
Mean and standard deviation for 10 and for 12 policies. In fact, the insurance company sees that in the entire population of homeowners, the mean loss from fire is μ = $300 and the standard deviation of the loss is σ = $400. What are the mean and standard deviation of the average loss for 10
Fire insurance. An insurance company looks at the records for millions of homeowners and sees that the mean loss from fire in a year is μ = $300 per person. (Most of us have no loss, but a few lose their homes. The $300 is the average loss.) The company plans to sell fire insurance for $300 plus
CHALLENG E A random variable with given mean and standard deviation. Here is a simple way to create a random variable X that has mean μ and standard deviation σ: X takes only the two valuesμ − σ and μ + σ, each with probability 0.5. Use the definition of the mean and variance for discrete

Showing 1700 - 1800 of 6020

First
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Last

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved