ELEMENTARY STATISTICS: STEP BY STEP- ALE
ELEMENTARY STATISTICS: STEP BY STEP- ALE
10th Edition
ISBN: 9781266422362
Author: Bluman
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Estimation
A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.
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Chapter 4.5, Problem 1AC

Applying the Concepts 4–5

Counting Rules and Probability

One of the biggest problems for students when doing probability problems is to decide which formula or formulas to use. Another problem is to decide whether two events are independent or dependent. Use the following problem to help develop a better understanding of these concepts.

Assume you are given a five-question multiple-choice quiz. Each question has 5 possible answers: A, B, C, D, and E.

1. How many events are there?

2. Are the events independent or dependent?

3. If you guess at each question, what is the probability that you get all of them correct?

4. What is the probability that a person guesses answer A for each question?

Assume that you are given a five-question matching test in which you are to match the correct answers in the right column with the questions in the left column. You can use each answer only once.

5. How many events are there?

6. Are the events independent or dependent?

7. What is the probability of getting them all correct if you are guessing?

8. What is the difference between the two problems?

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5. Let X and Y be independent random variables and let the superscripts denote symmetrization (recall Sect. 3.6). Show that (X + Y) X+ys.
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Chapter 4 Solutions

ELEMENTARY STATISTICS: STEP BY STEP- ALE

Ch. 4.1 - Tossing a Coin Assume you are at a carnival and...Ch. 4.1 - What is a probability experiment?Ch. 4.1 - Define sample space.Ch. 4.1 - What is the difference between an outcome and an...Ch. 4.1 - What are equally likely events?Ch. 4.1 - What is the range of the values of the probability...Ch. 4.1 - When an event is certain to occur, what is its...Ch. 4.1 - If an event cannot happen, what value is assigned...Ch. 4.1 - What is the sum of the probabilities of all the...Ch. 4.1 - If the probability that it will rain tomorrow is...
Ch. 4.1 - A probability experiment is conducted. Which of...Ch. 4.1 - Classify each statement as an example of classical...Ch. 4.1 - Classify each statement as an example of classical...Ch. 4.1 - Rolling a Die If a die is rolled one time, find...Ch. 4.1 - Rolling a Die If a die is rolled one time, find...Ch. 4.1 - Rolling Two Dice If two dice are rolled one time,...Ch. 4.1 - Rolling Two Dice If two dice are rolled one time,...Ch. 4.1 - Drawing a Card If one card is drawn from a deck,...Ch. 4.1 - Drawing a Card If a card is drawn from a deck,...Ch. 4.1 - Shopping Mall Promotion A shopping mall has set up...Ch. 4.1 - Selecting a State Choose one of the 50 states at...Ch. 4.1 - Human Blood Types Human blood is grouped into four...Ch. 4.1 - 2014 Top Albums (Based on U.S. sales) Of all of...Ch. 4.1 - Prime Numbers A prime number is a number that is...Ch. 4.1 - Rural Speed Limits Rural speed limits for all 50...Ch. 4.1 - Gender of Children A couple has 4 children. Find...Ch. 4.1 - Sources of Energy Uses in the United States A...Ch. 4.1 - Game of Craps In a game of craps, a player wins on...Ch. 4.1 - Computers in Elementary Schools Elementary and...Ch. 4.1 - College Debt The following information shows the...Ch. 4.1 - Population of Hawaii The population of Hawaii is...Ch. 4.1 - Crimes Committed The numbers show the number of...Ch. 4.1 - Living Arrangements for Children Here are the...Ch. 4.1 - Motor Vehicle Accidents During a recent year,...Ch. 4.1 - Federal Government Revenue The source of federal...Ch. 4.1 - Selecting a Bill A box contains a 1 bill, a 5...Ch. 4.1 - Tossing Coins Draw a tree diagram and determine...Ch. 4.1 - Prob. 37ECh. 4.1 - Family Dinner Combinations A family special at a...Ch. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Distribution of CEO Ages The distribution of ages...Ch. 4.1 - Tossing a Coin A person flipped a coin 100 times...Ch. 4.1 - Medical Treatment A medical doctor stated that...Ch. 4.1 - Wheel Spinner The wheel spinner shown here is spun...Ch. 4.1 - Tossing Coins Toss three coins 128 times and...Ch. 4.1 - Applying the Concepts 41 Tossing a Coin Assume you...Ch. 4.1 - Odds Odds are used in gambling games to make them...Ch. 4.2 - Applying the Concepts 42 Which Pain Reliever Is...Ch. 4.2 - Define mutually exclusive events, and give an...Ch. 4.2 - Explain briefly why addition rule 2 can be used...Ch. 4.2 - Cards, Dice, and Students Determine whether these...Ch. 4.2 - Determine whether these events are mutually...Ch. 4.2 - College Degrees Awarded The table below represents...Ch. 4.2 - Riding to School The probability that John will...Ch. 4.2 - Medical Specialities The following doctors were...Ch. 4.2 - U.S. Population The data show the U.S. population...Ch. 4.2 - Snack Foods In a meeting room in a dormitory there...Ch. 4.2 - Selecting a Movie A media rental store rented the...Ch. 4.2 - Pizza Sales A pizza restaurant sold 24 cheese...Ch. 4.2 - Selecting a Book At a used-book sale, 100 books...Ch. 4.2 - Young Adult Residences According to the Bureau of...Ch. 4.2 - Endangered Species The chart below shows the...Ch. 4.2 - Multiple Births The number of multiple births in...Ch. 4.2 - Licensed Drivers in the United States In a recent...Ch. 4.2 - Prison Education In a federal prison, inmates can...Ch. 4.2 - Mail Delivery A local postal carrier distributes...Ch. 4.2 - Medical Tests on Emergency Patients The frequency...Ch. 4.2 - College Fundraiser A social organization of 32...Ch. 4.2 - Emergency Room Tests The frequency distribution...Ch. 4.2 - Medical Patients A recent study of 300 patients...Ch. 4.2 - Selecting a Card If one card is drawn from an...Ch. 4.2 - Rolling Die Two dice are rolled. Find the...Ch. 4.2 - Apple Production For a recent year, about 11...Ch. 4.2 - Rolling Dice Three dice are rolled. Find the...Ch. 4.2 - Building a New Home In building new homes, a...Ch. 4.2 - Prob. 29ECCh. 4.2 - Prob. 30ECCh. 4.2 - Prob. 31ECCh. 4.2 - Events A and B are mutually exclusive with P(A)...Ch. 4.3 - State which events are independent and which are...Ch. 4.3 - State which events are independent and which are...Ch. 4.3 - Video and Computer Games Sixty-nine percent of...Ch. 4.3 - Seat Belt Use The Gallup Poll reported that 52% of...Ch. 4.3 - Automobile Sales An automobile salesperson finds...Ch. 4.3 - Prison Populations If 25% of U.S. federal prison...Ch. 4.3 - Government Employees In 2013 about 66% of...Ch. 4.3 - Working Women and Computer Use It is reported that...Ch. 4.3 - Female Prison Inmates Seventy-five percent of...Ch. 4.3 - Selecting Marbles A bag contains 9 red marbles, 8...Ch. 4.3 - Smart TVs Smart TVs have seen success in the...Ch. 4.3 - Flashlight Batteries A flashlight has 6 batteries,...Ch. 4.3 - Drawing a Card Four cards are drawn from a desk...Ch. 4.3 - Scientific Study In a scientific study there are 8...Ch. 4.3 - Drawing Cards If two cards are selected from a...Ch. 4.3 - Winning a Door Prize At a gathering consisting of...Ch. 4.3 - Defective Batteries In a box of 12 batteries, 2...Ch. 4.3 - Sales A manufacturer makes two models of an item:...Ch. 4.3 - Student Financial Aid In a recent year 8,073,000...Ch. 4.3 - Selecting Colored Balls Urn 1 contains 5 red balls...Ch. 4.3 - Automobile Insurance An insurance company...Ch. 4.3 - Defective Items A production process produces an...Ch. 4.3 - Prison Populations For a recent year, 0.99 of the...Ch. 4.3 - Rolling Dice Roll two standard dice and add the...Ch. 4.3 - Heart Disease Twenty-five percent of all deaths...Ch. 4.3 - Country Club Activities At the Avonlea Country...Ch. 4.3 - College Courses At a large university, the...Ch. 4.3 - Congressional Terms Below is given the summary...Ch. 4.3 - Pizza and Salads In a pizza restaurant, 95% of the...Ch. 4.3 - Gift Baskets The Gift Basket Store had the...Ch. 4.3 - Blood Types and Rh Factors In addition to being...Ch. 4.3 - Doctor Specialties Below are listed the numbers of...Ch. 4.3 - Lightning Strikes It has been said that the...Ch. 4.3 - Foreign Adoptions The following foreign adoptions...Ch. 4.3 - Leisure Time Exercise Only 27% of U.S. adults get...Ch. 4.3 - Customer Purchases In a department store there are...Ch. 4.3 - Marital Status of Women According to the...Ch. 4.3 - Fatal Accidents The American Automobile...Ch. 4.3 - On-Time Airplane Arrivals According to FlightStats...Ch. 4.3 - On-Time Flights A flight from Pittsburgh to...Ch. 4.3 - Reading to Children Fifty-eight percent of...Ch. 4.3 - Doctoral Assistantships Of Ph.D. students, 60%...Ch. 4.3 - Prob. 43ECh. 4.3 - Autism In recent years it was thought that...Ch. 4.3 - Video Game. Video games are rated according to the...Ch. 4.3 - Medication Effectiveness A medication is 75%...Ch. 4.3 - Selecting Digits If 3 digits are selected at...Ch. 4.3 - Selecting a Letter of the Alphabet If 3 letters of...Ch. 4.3 - Rolling a Die A die is rolled twice. Find the...Ch. 4.3 - U.S. Organ Transplants As of June 2015, 81.4% of...Ch. 4.3 - Lucky People Twelve percent of people in Western...Ch. 4.3 - Selecting a Flower In a large vase, there are 8...Ch. 4.3 - Let A and B be two mutually exclusive events. Are...Ch. 4.3 - Types of Vehicles The Bargain Auto Mall has the...Ch. 4.3 - Commercials Event A is the event that a person...Ch. 4.3 - Given a sample space with events A and B such that...Ch. 4.3 - Childs Board Game In a childs board game of the...Ch. 4.3 - Bags Containing Marbles Two bags contain marbles....Ch. 4.4 - Garage Door Openers Garage door openers originally...Ch. 4.4 - Zip Codes How many 5-digit zip codes are possible...Ch. 4.4 - Letter Permutations List all the permutations of...Ch. 4.4 - Speaking Order Seven elementary students are...Ch. 4.4 - Visiting Nurses How many different ways can a...Ch. 4.4 - Quinto Lottery A lottery game called Quinto is...Ch. 4.4 - Show Programs Three bands and two comics are...Ch. 4.4 - Rolling Dice If five dice are rolled, how many...Ch. 4.4 - Radio Station Call Letters The call letters of a...Ch. 4.4 - Film Showings At the Rogue Film Festival, the...Ch. 4.4 - Secret Code Word How many 4-letter code words can...Ch. 4.4 - Passwords Given the characters A, B, C, H, I, T,...Ch. 4.4 - Automobile Trips There are 2 major roads from city...Ch. 4.4 - Evaluate each expression. a. 11! b. 9! c. 0! d. 1!...Ch. 4.4 - Evaluate each expression. a. 6! b. 11! c. 2! d. 9!...Ch. 4.4 - Sports Car Stripes How many different 4-color code...Ch. 4.4 - Manufacturing Tests An inspector must select 3...Ch. 4.4 - Endangered Amphibians There are 9 endangered...Ch. 4.4 - Inspecting Restaurants How many different ways can...Ch. 4.4 - Word Permutation How many different 4-letter...Ch. 4.4 - Word Permutation How many different 4-letter...Ch. 4.4 - ID Cards How many different ID cards can be made...Ch. 4.4 - Free-Sample Requests An online coupon service has...Ch. 4.4 - Ticket Selection How many different ways can 4...Ch. 4.4 - Movie Selections The Foreign Language Club is...Ch. 4.4 - Task Assignments How many ways can an adviser...Ch. 4.4 - Agency Cases An investigative agency has 7 cases...Ch. 4.4 - Signal Flags How many different flag signals, each...Ch. 4.4 - Word Permutations How many permutations can be...Ch. 4.4 - Code Words How many different 9-letter code words...Ch. 4.4 - Toothpaste Display How many different ways can 5...Ch. 4.4 - Book Arrangements How many different ways can 6...Ch. 4.4 - Word Permutations How many permutations can be...Ch. 4.4 - Evaluate each expression. a. 5C2 b. 8C3 c. 7C4 d....Ch. 4.4 - Evaluate each expression. a. 3C0 b. 3C3 c. 9C7 d....Ch. 4.4 - Medications for Depression A researcher wishes her...Ch. 4.4 - Selecting Players How many ways can 4 baseball...Ch. 4.4 - Coffee Selection A coffee shop serves 12 different...Ch. 4.4 - Selecting Christmas Presents If a person can...Ch. 4.4 - Buffet Desserts In how many ways can you choose 3...Ch. 4.4 - Bridge Foursomes How many different tables of 4...Ch. 4.4 - Music Recital Six students are performing one song...Ch. 4.4 - Freight Train Cars In a train yard there are 4...Ch. 4.4 - Selecting a Committee There are 7 women and 5 men...Ch. 4.4 - Buffet Desserts In how many ways can you choose 3...Ch. 4.4 - Hawaiian Words The Hawaiian alphabet consists of 7...Ch. 4.4 - Selecting a Jury How many ways can a jury of 6...Ch. 4.4 - Selecting Students How many ways can you pick 4...Ch. 4.4 - Investigative Team The state narcotics bureau must...Ch. 4.4 - Prob. 49ECh. 4.4 - Charity Event Participants There are 16 seniors...Ch. 4.4 - Automobile Selection An automobile dealer has 12...Ch. 4.4 - DVD Selection How many ways can a person select 8...Ch. 4.4 - Railroad Accidents A researcher wishes to study...Ch. 4.4 - Selecting a Location An advertising manager...Ch. 4.4 - Prob. 55ECh. 4.4 - Test Marketing Products Anderson Research Company...Ch. 4.4 - Prob. 57ECh. 4.4 - Selecting Musicals How many different ways can a...Ch. 4.4 - Textbook Selection How many different ways can an...Ch. 4.4 - DVD Selection How many ways can a person select 8...Ch. 4.4 - Prob. 61ECh. 4.4 - Signal Flags How many different signals can be...Ch. 4.4 - Prob. 63ECh. 4.4 - Air Pollution The Environmental Protection Agency...Ch. 4.4 - Selecting Officers In a board of directors...Ch. 4.4 - Prob. 67ECCh. 4.4 - Prob. 68ECCh. 4.4 - Seating in a Movie Theater How many different ways...Ch. 4.4 - Prob. 70ECCh. 4.4 - Prob. 71ECCh. 4.4 - Prob. 72ECCh. 4.5 - Applying the Concepts 45 Counting Rules and...Ch. 4.5 - Selecting Cards Find the probability of getting 2...Ch. 4.5 - Selecting Cards Cards numbered 110 are shuffled...Ch. 4.5 - Educational Fellowship A university received 9...Ch. 4.5 - Senate Partisanship The composition of the Senate...Ch. 4.5 - Job Applications Six men and seven women apply for...Ch. 4.5 - Defective Resistors A package contains 12...Ch. 4.5 - Winning Tickets At a meeting of 10 executives (7...Ch. 4.5 - Getting a Full House Find the probability of...Ch. 4.5 - World-Class Orchestras About.coms list of 20 World...Ch. 4.5 - Selecting Cards The red face cards and the black...Ch. 4.5 - Socks in a Drawer A drawer contains 11 identical...Ch. 4.5 - Selecting Books Find the probability of selecting...Ch. 4.5 - Rolling the Dice If three dice are rolled, find...Ch. 4.5 - Football Team Selection A football team consists...Ch. 4.5 - Arrangement of Washers Find the probability that...Ch. 4.5 - Poker Hands Using the information in Exercise 70...Ch. 4.5 - Prob. 17ECh. 4 - Rolling a Die An eight-sided die is rolled. Find...Ch. 4 - Selecting a Card When a card is selected from a...Ch. 4 - Software Selection The top-10 selling computer...Ch. 4 - Motor Vehicle Producers The top five motor vehicle...Ch. 4 - Exercise Preference In a local fitness club, 32%...Ch. 4 - Rolling Two Dice When two dice are rolled, find...Ch. 4 - New Cars The probability that a new automobile has...Ch. 4 - Breakfast Drink In a recent survey, 18 people...Ch. 4 - Lawnmower and Weed Wacker Ownership The...Ch. 4 - Casino Gambling The probability that a gambler...Ch. 4 - Online Course Selection Roughly 1 in 6 students...Ch. 4 - Purchasing Sweaters During a sale at a mens store,...Ch. 4 - Drawing Cards Three cards are drawn from an...Ch. 4 - Coin Toss and Card Drawn A coin is tossed and a...Ch. 4 - Movie Releases The top five countries for movie...Ch. 4 - Factory Output A manufacturing company has three...Ch. 4 - Effectiveness of Vaccine A vaccine has a 90%...Ch. 4 - T-shirt Factories Two T-shirt printing factories...Ch. 4 - Car Purchase The probability that Sue will live on...Ch. 4 - Prob. 4.3.20RECh. 4 - Prob. 4.3.21RECh. 4 - Bad Weather The probability that it snows and the...Ch. 4 - Education Level and Smoking At a large factory,...Ch. 4 - Prob. 4.3.24RECh. 4 - Television Sets If 98% of households have at least...Ch. 4 - Prob. 4.3.26RECh. 4 - Motorcycle License Plates If a motorcycle license...Ch. 4 - Prob. 4.4.28RECh. 4 - Prob. 4.4.29RECh. 4 - Prob. 4.4.30RECh. 4 - Prob. 4.4.31RECh. 4 - Committee Representation There are 6 Republican, 5...Ch. 4 - Song Selections A promotional MP3 player is...Ch. 4 - Prob. 4.4.34RECh. 4 - Prob. 4.4.35RECh. 4 - Prob. 4.4.36RECh. 4 - Prob. 4.4.37RECh. 4 - Prob. 4.4.38RECh. 4 - Movie Selections If a person can select one movie...Ch. 4 - Prob. 4.4.40RECh. 4 - Catalog ID Numbers In a catalog, movies are...Ch. 4 - License Plates A certain states license plate has...Ch. 4 - Territorial Selection Several territories and...Ch. 4 - Yahtzee Yahtzee is a game played with 5 dice....Ch. 4 - Personnel Classification For a survey, a subject...Ch. 4 - Determine whether each statement is true or false....Ch. 4 - Determine whether each statement is true or false....Ch. 4 - Prob. 3CQCh. 4 - Prob. 4CQCh. 4 - Determine whether each statement is true or false....Ch. 4 - Determine whether each statement is true or false....Ch. 4 - Prob. 7CQCh. 4 - Prob. 8CQCh. 4 - Prob. 9CQCh. 4 - When a meteorologist says that there is a 30%...Ch. 4 - The sample space for tossing 3 coins consists of...Ch. 4 - Prob. 12CQCh. 4 - When two dice are rolled, the sample space...Ch. 4 - Prob. 14CQCh. 4 - What is the number of permutations of 6 different...Ch. 4 - Prob. 16CQCh. 4 - Prob. 17CQCh. 4 - Complete the following statements with the best...Ch. 4 - Complete the following statements with the best...Ch. 4 - Complete the following statements with the best...Ch. 4 - Complete the following statements with the best...Ch. 4 - Complete the following statements with the best...Ch. 4 - Prob. 23CQCh. 4 - Selecting a Card When a card is drawn from a deck,...Ch. 4 - Selecting a Sweater At a mens clothing store, 12...Ch. 4 - Prob. 26CQCh. 4 - Appliance Ownership The probability that a person...Ch. 4 - Starting Salaries Of the physics graduates of a...Ch. 4 - Prob. 29CQCh. 4 - Scholarships The probability that Samantha will be...Ch. 4 - Prob. 31CQCh. 4 - Prob. 32CQCh. 4 - Work and Weather The probability that Mike has to...Ch. 4 - Education of Factory Employees At a large factory,...Ch. 4 - Heart Attacks In a certain high-risk group, the...Ch. 4 - Rolling a Die A single die is rolled 4 times. Find...Ch. 4 - Prob. 37CQCh. 4 - Singer Selection How many ways can 5 sopranos and...Ch. 4 - Speaker Selection How many different ways can 8...Ch. 4 - Stocking Machines A soda machine servicer must...Ch. 4 - ID Cards One companys ID cards consist of 5...Ch. 4 - Prob. 42CQCh. 4 - Prob. 43CQCh. 4 - Prob. 44CQCh. 4 - Prob. 45CQCh. 4 - Cruise Ship Activities A cruise director schedules...Ch. 4 - Prob. 47CQCh. 4 - Prob. 48CQCh. 4 - Toy Display A toy store manager wants to display 7...Ch. 4 - Commercial Order A local television station must...Ch. 4 - Prob. 1CTCCh. 4 - Prob. 2CTCCh. 4 - Prob. 3CTCCh. 4 - Prob. 4CTC
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