Binomial n 25 p 0.33 xi P(X<=xi) 0 0.0000 1 0.0006 2 0.0039 3 0.0162 4 0.0496 5

Question

Binomial  

  

n  

25  

p  

0.33  

  

  

xi  

P(X<=xi)  

0  

0.0000  

1  

0.0006  

2  

0.0039  

3  

0.0162  

4  

0.0496  

5  

0.1187  

6  

0.2321  

7  

0.3837  

8  

0.5518  

9  

0.7081  

10  

0.8314  

11  

0.9141  

12  

0.9617  

13  

0.9851  

14  

0.9950  

15  

0.9985  

16  

0.9996  

17  

0.9999  

18  

1.0000  

19  

1.0000  

20  

1.0000  

21  

1.0000  

22  

1.0000  

23  

1.0000  

24  

1.0000  

25  

1.0000  

Use the cumulative binomial probability excel output above (dealing with the number of Americans who are satisfied with the way things are going in the U.S.) to answer the following question. (See exercise 42 on page 253 in your textbook for similar problem.)

Find the probability that at least 16 Americans are not satisfied with the way things are going.

Binomial  

  

n  

25  

p  

0.33  

  

  

xi  

P(X<=xi)  

0  

0.0000  

1  

0.0006  

2  

0.0039  

3  

0.0162  

4  

0.0496  

5  

0.1187  

6  

0.2321  

7  

0.3837  

8  

0.5518  

9  

0.7081  

10  

0.8314  

11  

0.9141  

12  

0.9617  

13  

0.9851  

14  

0.9950  

15  

0.9985  

16  

0.9996  

17  

0.9999  

18  

1.0000  

19  

1.0000  

20  

1.0000  

21  

1.0000  

22  

1.0000  

23  

1.0000  

24  

1.0000  

25  

1.0000  

Explanation / Answer

P(Atleast 16 Americans are not satisfied)

= 1 - P(Less than 16 Americans are not satisfied)

= 1 - P(More than 9 Americans are satisfied)

= 1 - (1 - P(X < 9))

= 0.7081

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