Elementary Statistics: A Step-by-Step Approach with Formula Card
Elementary Statistics: A Step-by-Step Approach with Formula Card
9th Edition
ISBN: 9780078136337
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Chapter 5.4, Problem 2E

Use the multinomial formula and find the probabilities for each.

a. n = 3, X1 = 1, X2 = 1, X3 = 1, p1 = 0.5, p2 = 0.3, p3 = 0.2

b. n = 5, X1 = 1, X2 = 3, X3 = 1, p1 = 0.7, p2 = 0.2, p3 = 0.1

c. n = 7, X1 = 2, X2 = 3, X3 = 2, p1 = 0.4, p2 = 0.5, p3 = 0.1

a.

Expert Solution
Check Mark
To determine

The probability, P(X)

Answer to Problem 2E

P(X)=0.18_

Explanation of Solution

Given info:

When the values are n=3,X1=1,X2=1,X3=1,p1=0.5,p2=0.3 and p3=0.2

Calculation:

The formula for multinomial distribution is given below:

P(X)=n!X1!X2!X3!Xk!p1X1p2X2p3X3pkXk

Where, X1+X1+...+Xk=1 and p1+p2+...+pk=1

Substitute n as 3,X1 as 1,X2 as 1,X3 as 1,p1 as 0.5,p2 as 0.3 and p3 as 0.2

P(X)=3!1!1!1!(0.5)1(0.3)1(0.2)1=6(0.5)(0.3)(0.2)=0.18

b.

Expert Solution
Check Mark
To determine

The probability, P(X)

Answer to Problem 2E

P(X)=0.112_

Explanation of Solution

Given info:

When the values are n=5,X1=1,X2=3,X3=1,p1=0.7,p2=0.2 and p3=0.1

Calculation:

Substitute n as 5,X1 as 1,X2 as 3,X3 as 1,p1 as 0.7,p2 as 0.2 and p3 as 0.1

P(X)=5!1!3!1!(0.7)1(0.2)3(0.1)1=1206(0.7)(0.008)(0.1)=20(0.7)(0.008)(0.1)=0.112

c.

Expert Solution
Check Mark
To determine

The probability, P(X)

Answer to Problem 2E

P(X)=0.036_

Explanation of Solution

Given info:

When the values are n=7,X1=2,X2=3,X3=2,p1=0.4,p2=0.5 and p3=0.1

Calculation:

Substitute n as 7,X1 as 2,X2 as 2,X3 as 2,p1 as 0.4,p2 as 0.5 and p3 as 0.1

P(X)=7!2!3!2!(0.4)2(0.3)3(0.1)2=5,0406(0.16)(0.027)(0.01)=840(0.0000432)=0.036

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Chapter 5 Solutions

Elementary Statistics: A Step-by-Step Approach with Formula Card

Ch. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - Prob. 11ECh. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - Prob. 13ECh. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - Prob. 15ECh. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - Prob. 17ECh. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - Prob. 19ECh. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - Prob. 21ECh. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - Triangular Numbers The first six triangular...Ch. 5.1 - Prob. 28ECh. 5.1 - Goals in Hockey The probability that a hockey team...Ch. 5.1 - Mathematics Tutoring Center At a drop-in...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - Computer Games The probability that a child plays...Ch. 5.2 - Radiation Exposure On March 28, 1979, the nuclear...Ch. 5.2 - Prob. 1ECh. 5.2 - Suit Sales The number of suits sold per day at a...Ch. 5.2 - Prob. 3ECh. 5.2 - Trivia Quiz The probabilities that a player will...Ch. 5.2 - Prob. 5ECh. 5.2 - Traffic Accidents The county highway department...Ch. 5.2 - Prob. 7ECh. 5.2 - Benfords Law The leading digits in actual data,...Ch. 5.2 - Prob. 9ECh. 5.2 - Pizza Deliveries A pizza shop owner determines the...Ch. 5.2 - Prob. 11ECh. 5.2 - Job Bids A landscape contractor bids on jobs where...Ch. 5.2 - Rolling Dice If a person rolls doubles when she...Ch. 5.2 - Dice Game A person pays 2 to play a certain game...Ch. 5.2 - Lottery Prizes A lottery offers one 1000 prize,...Ch. 5.2 - Winning the Lottery For a daily lottery, a person...Ch. 5.2 - Life Insurance A 35-year-old woman purchases a...Ch. 5.2 - Roulette A roulette wheel has 38 numbers, 1...Ch. 5.2 - Rolling Dice Construct a probability distribution...Ch. 5.2 - Rolling a Die When one die is rolled, the expected...Ch. 5.2 - The formula for finding the variance for a...Ch. 5.2 - Complete the following probability distribution if...Ch. 5.2 - Probability Distribution A bag contains five balls...Ch. 5.3 - Unsanitary Restaurants Health officials routinely...Ch. 5.3 - Which of the following are binomial experiments or...Ch. 5.3 - Which of the following are binomial experiments or...Ch. 5.3 - Compute the probability of X successes, using...Ch. 5.3 - Compute the probability of X successes, using...Ch. 5.3 - Compute the probability of X successes, using the...Ch. 5.3 - Compute the probability of X successes, using the...Ch. 5.3 - Prob. 7ECh. 5.3 - Multiple-Choice Exam A student takes a...Ch. 5.3 - Prob. 9ECh. 5.3 - High School Dropouts Approximately 10.3% of...Ch. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Destination Weddings Twenty-six percent of couples...Ch. 5.3 - People Who Have Some College Education Fifty-three...Ch. 5.3 - Guidance Missile System A missile guidance system...Ch. 5.3 - Find the mean, variance, and standard deviation...Ch. 5.3 - Find the mean, variance, and standard deviation...Ch. 5.3 - Prob. 19ECh. 5.3 - Tossing Coins Find the mean, variance, and...Ch. 5.3 - Prob. 21ECh. 5.3 - Federal Government Employee E-mail Use It has been...Ch. 5.3 - Watching Fireworks A survey found that 21% of...Ch. 5.3 - Alternate Sources of Fuel Eighty-five percent of...Ch. 5.3 - Survey on Bathing Pets A survey found that 25% of...Ch. 5.3 - Survey on Answering Machine Ownership In a survey,...Ch. 5.3 - Poverty and the Federal Government One out of...Ch. 5.3 - Internet Purchases Thirty-two percent of adult...Ch. 5.3 - Prob. 29ECh. 5.3 - Job Elimination In a recent year, 13% of...Ch. 5.3 - Survey of High School Seniors Of graduating high...Ch. 5.3 - Is this a binomial distribution? 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What is the sum of the...Ch. 5 - Select the best answer. 9. How many outcomes are...Ch. 5 - Select the best answer. 10. The number of trials...Ch. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - For exercises 11 through 14, determine if the...Ch. 5 - For exercises 11 through 14, determine if the...Ch. 5 - Prob. 15CQCh. 5 - Prob. 16CQCh. 5 - Prob. 17CQCh. 5 - Calls for a Crisis Hot Line The number of calls...Ch. 5 - Selecting a Card There are 6 playing cards placed...Ch. 5 - Prob. 20CQCh. 5 - Carpooling If 40% of all commuters ride to work in...Ch. 5 - Employed Women If 60% of all women are employed...Ch. 5 - Prob. 23CQCh. 5 - Meeting Attendance A history class has 75 members....Ch. 5 - Prob. 25CQCh. 5 - Quality Control Check Before a television set...Ch. 5 - Bowling Team Uniforms Among the teams in a bowling...Ch. 5 - Elm Trees If 8% of the population of trees are elm...Ch. 5 - Sports Score Hot Line Calls Sports Scores Hot Line...Ch. 5 - Color of Raincoats There are 48 raincoats for sale...Ch. 5 - Youth Group Officers A youth group has 8 boys and...Ch. 5 - Blood Types About 4% of the citizens of the United...Ch. 5 - Alcohol Abstainers About 35% of Americans abstain...Ch. 5 - Prob. 1CTCCh. 5 - Prob. 2CTCCh. 5 - Prob. 3CTCCh. 5 - Prob. 4CTCCh. 5 - Prob. 5CTC
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