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In a recent study 90 percent of the homes in the United

Basic Statistics for Business and Economics | 7th Edition | ISBN: 9780077384470 | Authors: Douglas Lind; William Marchal; Samuel Wathen ISBN: 9780077384470 64

Solution for problem 21E Chapter 6

Basic Statistics for Business and Economics | 7th Edition

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Basic Statistics for Business and Economics | 7th Edition | ISBN: 9780077384470 | Authors: Douglas Lind; William Marchal; Samuel Wathen

Basic Statistics for Business and Economics | 7th Edition

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1
Problem 21E

Problem 21E

In a recent study 90 percent of the homes in the United States were found to have large- screen TVs. In a sample of nine homes, what is the probability that:

a. All nine have large-screen TVs?

b. Less than five have large-screen TVs?

c. More than five have large-screen TVs?

d. At least seven homes have large-screen TVs?

Step-by-Step Solution:
Step 1 of 3

Solution 21E

Step1 of 5:

Let us consider a random variable ‘X’ it presents the number of homes in the United States were found to have large- screen TV’s. Also, we have ‘n = 9 and ’.

Here our goal is:

a). We need to find the probability that all nine have large-screen TV’s.

b). We need to find the probability that less than five have large-screen TV’s.

c). We need to find the probability that more than five have large-screen TV’s.

d). We need to find the probability at least seven homes have large-screen TV’s.


Step2 of 5:

a).

We know that ‘x’ follows a binomial distribution with parameters ‘n = 9 and ’. Then, the probability mass function of the binomial distribution is:

                       

Now,

 

                                                     

Therefore, P(X = 9) = 0.3875.


Step3 of 5:

b).

The probability that less than five have large-screen TV’s is:

 

Where, is obtained from Excel by using the function “=Binomdist(X,n,false)” 

X

P(X < 5)

1

8.1E-08

2

2.92E-06

3

6.12E-05

4

0.000827

Total

0.000891

Therefore, P(X < 5) = 0.000891.


Step4 of 5:

c).

The probability that more than five have large-screen TV’s is:

 

Where,

Where, is obtained from Excel by using the function “=Binomdist(X,n,false)” 

X

P(X5)

1

8.1E-08

2

2.92E-06

3

6.12E-05

4

0.000827

5

0.00744

Total

0.008331

Therefore, P(X5) = 0.008331.

Now,

 

                 

         

Therefore,


Step5 of 5:

d).

The probability at least seven homes have large-screen TV’s is:

 

Where,

Where, is obtained from Excel by using the function “=Binomdist(X,n,false)” 

X

P(X < 7)

1

8.1E-08

2

2.92E-06

3

6.12E-05

4

0.000827

5

0.00744

6

0.044641

Total

0.0530

Therefore, P(X < 5) = 0.0530.

Now,

 

             

       

Therefore,


Step 2 of 3

Chapter 6, Problem 21E is Solved
Step 3 of 3

Textbook: Basic Statistics for Business and Economics
Edition: 7
Author: Douglas Lind; William Marchal; Samuel Wathen
ISBN: 9780077384470

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