Historical data indicates that only 20 of cable customers ar

Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that

Between 2 and 5 (inclusive) customers are willing to switch companies?

Less than 5 customers are willing to switch

More than 16 customers are willing to switch

Solution

Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that

p=0.2

n=20

Binomial Probabilities

Data

Sample size

20

Probability of an event of interest

0.2

Statistics

Mean

4

Variance

3.2000

Standard deviation

1.7889

Binomial Probabilities Table

X

P(X)

P(<=X)

P(<X)

P(>X)

P(>=X)

0

0.0115

0.0115

0.0000

0.9885

1.0000

1

0.0576

0.0692

0.0115

0.9308

0.9885

2

0.1369

0.2061

0.0692

0.7939

0.9308

3

0.2054

0.4114

0.2061

0.5886

0.7939

4

0.2182

0.6296

0.4114

0.3704

0.5886

5

0.1746

0.8042

0.6296

0.1958

0.3704

6

0.1091

0.9133

0.8042

0.0867

0.1958

7

0.0545

0.9679

0.9133

0.0321

0.0867

8

0.0222

0.9900

0.9679

0.0100

0.0321

9

0.0074

0.9974

0.9900

0.0026

0.0100

10

0.0020

0.9994

0.9974

0.0006

0.0026

11

0.0005

0.9999

0.9994

0.0001

0.0006

12

0.0001

1.0000

0.9999

0.0000

0.0001

13

0.0000

1.0000

1.0000

0.0000

0.0000

14

0.0000

1.0000

1.0000

0.0000

0.0000

15

0.0000

1.0000

1.0000

0.0000

0.0000

16

0.0000

1.0000

1.0000

0.0000

0.0000

17

0.0000

1.0000

1.0000

0.0000

0.0000

18

0.0000

1.0000

1.0000

0.0000

0.0000

19

0.0000

1.0000

1.0000

0.0000

0.0000

20

0.0000

1.0000

1.0000

0.0000

0.0000

Between 2 and 5 (inclusive) customers are willing to switch companies?

P( 2<=x<=5)=P(x=2)+P( x=3)+P(x=4)+P( x=5)

=

= 0.7351

Less than 5 customers are willing to switch

P( x <5)= P( x=0)+P( x=1)+ P(x=2)+P( x=3)+P(x=4)

=0.0115+0.0576+0.1369+0.2054+0.2182

=0.6296

More than 16 customers are willing to switch

P( x >16)= P( x=17)+P( x=18)+ P(x=19)+P( x=20)

=0+0+0+0

=0.0000

Binomial Probabilities
Data
Sample size	20
Probability of an event of interest	0.2
Statistics
Mean	4
Variance	3.2000
Standard deviation	1.7889
Binomial Probabilities Table
	X	P(X)	P(<=X)	P(<X)	P(>X)	P(>=X)
	0	0.0115	0.0115	0.0000	0.9885	1.0000
	1	0.0576	0.0692	0.0115	0.9308	0.9885
	2	0.1369	0.2061	0.0692	0.7939	0.9308
	3	0.2054	0.4114	0.2061	0.5886	0.7939
	4	0.2182	0.6296	0.4114	0.3704	0.5886
	5	0.1746	0.8042	0.6296	0.1958	0.3704
	6	0.1091	0.9133	0.8042	0.0867	0.1958
	7	0.0545	0.9679	0.9133	0.0321	0.0867
	8	0.0222	0.9900	0.9679	0.0100	0.0321
	9	0.0074	0.9974	0.9900	0.0026	0.0100
	10	0.0020	0.9994	0.9974	0.0006	0.0026
	11	0.0005	0.9999	0.9994	0.0001	0.0006
	12	0.0001	1.0000	0.9999	0.0000	0.0001
	13	0.0000	1.0000	1.0000	0.0000	0.0000
	14	0.0000	1.0000	1.0000	0.0000	0.0000
	15	0.0000	1.0000	1.0000	0.0000	0.0000
	16	0.0000	1.0000	1.0000	0.0000	0.0000
	17	0.0000	1.0000	1.0000	0.0000	0.0000
	18	0.0000	1.0000	1.0000	0.0000	0.0000
	19	0.0000	1.0000	1.0000	0.0000	0.0000
	20	0.0000	1.0000	1.0000	0.0000	0.0000