Binomial n 25 p 0.39 xi P(X<=xi) 0 0.0000 1 0.0001 2 0.0006 3 0.0032 4 0.0123 5

Question

Binomial  

  

n  

25  

p  

0.39  

  

  

xi  

P(X<=xi)  

0  

0.0000  

1  

0.0001  

2  

0.0006  

3  

0.0032  

4  

0.0123  

5  

0.0367  

6  

0.0886  

7  

0.1789  

8  

0.3086  

9  

0.4653  

10  

0.6257  

11  

0.7654  

12  

0.8697  

13  

0.9363  

14  

0.9729  

15  

0.9900  

16  

0.9968  

17  

0.9992  

18  

0.9998  

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 more than 40% but at most 75% of these Americans are satisfied with the way things are going.

Binomial  

  

n  

25  

p  

0.39  

  

  

xi  

P(X<=xi)  

0  

0.0000  

1  

0.0001  

2  

0.0006  

3  

0.0032  

4  

0.0123  

5  

0.0367  

6  

0.0886  

7  

0.1789  

8  

0.3086  

9  

0.4653  

10  

0.6257  

11  

0.7654  

12  

0.8697  

13  

0.9363  

14  

0.9729  

15  

0.9900  

16  

0.9968  

17  

0.9992  

18  

0.9998  

19  

1.0000  

20  

1.0000  

21  

1.0000  

22  

1.0000  

23  

1.0000  

24  

1.0000  

25  

1.0000  

Explanation / Answer

probability that more than 40% but at most 75% of these Americans are satisfied with the way things are going

Here, n=25 (not specified so assuming this is count of American's from a sample)

40% of 25 = 25*0.4 = 10

75% of 25 = 25*0.75 18.75

we need at most 75% so rounding off to 18

Thus, Required probability = P(10<n<=18)

= 0.9998 - 0.6257

= 0.3741

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