Elementary Statistics: A Step By Step Approach
Elementary Statistics: A Step By Step Approach
10th Edition
ISBN: 9781259755330
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Chapter 5.4, Problem 1E

Use the multinomial formula and find the probabilities for each.

a. n = 6, X1 = 3, X2 = 2, X3 = 1, p1 = 0.5, p2 = 0.3, p3 = 0.2

b. n = 5, X1 = 1, X2 = 2, X3 = 2, p1 = 0.3, p2 = 0.6, p3 = 0.1

c. n = 4, X1 = 1, X2 = 1, X3 = 2, p1 = 0.8, p2 = 0.1, p3 = 0.1

a.

Expert Solution
Check Mark
To determine

To find: The probability, P(X)

Answer to Problem 1E

P(X)=0.135_

Explanation of Solution

Given info:

The given values are n=6,X1=3,X2=2,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+X2+X3++Xk=n and p1+p2+p3+...+pk=1

Substitute n as 6, X1 as 3, X2 as 2, X3 as 1 and p1 as 0.5,p2 as 0.3 and p3 as 0.2

P(X)=6!3!2!1!(0.5)3(0.3)2(0.2)1=72012(0.125)(0.09)(0.2)=60(0.125)(0.09)(0.2)=0.135

b.

Expert Solution
Check Mark
To determine

To find: The probability, P(X)

Answer to Problem 1E

P(X)=0.0324_

Explanation of Solution

Given info:

The given values are n=5,X1=1,X2=2,X3=2,p1=0.3,p2=0.6 and p3=0.1

Calculation:

Substitute n as 5, X1 as 1, X2 as 2, X3 as 2 and p1 as 0.3,p2 as 0.6 and p3 as 0.1

P(X)=5!1!2!2!(0.3)1(0.6)2(0.1)2=1204(0.3)(0.36)(0.01)=30(0.00108)=0.0324

c.

Expert Solution
Check Mark
To determine

To find: The probability, P(X)

Answer to Problem 1E

P(X)=0.0096_

Explanation of Solution

Given info:

The given values are n=4,X1=1,X2=1,X3=2,p1=0.8,p2=0.1 and p3=0.1

Calculation:

Substitute n as 4, X1 as 1, X2 as 1, X3 as 2 and p1 as 0.8,p2 as 0.1 and p3 as 0.1

P(X)=4!1!1!2!(0.8)1(0.1)1(0.1)2=242(0.8)(0.1)(0.01)=12(0.0008)=0.0096

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Chapter 5 Solutions

Elementary Statistics: A Step By Step Approach

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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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