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Binomial n 25 p 0.36 xi P(X<=xi) 0 0.0000 1 0.0002 2 0.0016 3 0.0074 4 0.0255 5

ID: 3071613 • Letter: B

Question

Binomial  

  

n  

25  

p  

0.36  

  

  

xi  

P(X<=xi)  

0  

0.0000  

1  

0.0002  

2  

0.0016  

3  

0.0074  

4  

0.0255  

5  

0.0682  

6  

0.1483  

7  

0.2705  

8  

0.4252  

9  

0.5896  

10  

0.7376  

11  

0.8510  

12  

0.9255  

13  

0.9674  

14  

0.9876  

15  

0.9959  

16  

0.9989  

17  

0.9997  

18  

0.9999  

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 the number of Americans who are satisfied with the way things are going differs by greater than 1 from the mean.

Binomial  

  

n  

25  

p  

0.36  

  

  

xi  

P(X<=xi)  

0  

0.0000  

1  

0.0002  

2  

0.0016  

3  

0.0074  

4  

0.0255  

5  

0.0682  

6  

0.1483  

7  

0.2705  

8  

0.4252  

9  

0.5896  

10  

0.7376  

11  

0.8510  

12  

0.9255  

13  

0.9674  

14  

0.9876  

15  

0.9959  

16  

0.9989  

17  

0.9997  

18  

0.9999  

19  

1.0000  

20  

1.0000  

21  

1.0000  

22  

1.0000  

23  

1.0000  

24  

1.0000  

25  

1.0000  

Explanation / Answer

Mean = 25*0.36 = 9

So,

P(Differs greater than 1 from mean)

= 1 - P(Within 1 from mean)

= 1 - P(8 < X < 10)

= 1 - [F(10) - F(7)]

= 1 - (0.7376 - 0.2705)

= 0.5329