The speed with which utility companies can resolve problems

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 68% of the cases. Suppose the 14 cases reported today are representative of all complaints.

How many of the problems would you expect to be resolved today? (Round your answer to 2 decimal places.)

What is the probability 8 of the problems can be resolved today? (Round your answer to 4 decimal places.)

What is the probability 8 or 9 of the problems can be resolved today? (Round your answer to 4 decimal places.)

  

What is the probability more than 9 of the problems can be resolved today? (Round your answer to 4 decimal places.)

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 68% of the cases. Suppose the 14 cases reported today are representative of all complaints.

Solution

the speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 68% of the cases. Suppose the 14 cases reported today are representative of all complaints.

Binomial distribution used

n=14

P=0.68

a-1. How many of the problems would you expect to be resolved today? (Round your answer to 2 decimal places.)

Expectation = np = 9.52

                Number of Problems =9.52

a-2.        What is the standard deviation? (Round your answer to 4 decimal places.)

Variance = np(1 - p) = 3.0464

Standard deviation = 1.7454

                Standard Deviation =1.7454    

Binomial Probabilities Tablefor p=0.68

X

P(X)

0

0.0000

1

0.0000

2

0.0000

3

0.0004

4

0.0024

5

0.0102

6

0.0326

7

0.0793

8

0.1474

9

0.2088

10

0.2219

11

0.1715

12

0.0911

13

0.0298

14

0.0045

b.            What is the probability 8 of the problems can be resolved today? (Round your answer to 4 decimal places.)

Probability        P(x=8) =0.1474

c.             What is the probability 8 or 9 of the problems can be resolved today? (Round your answer to 4 decimal places.)

                Probability       P( x=8 or x=9) =0.1474+0.2088 =0.3562

d.            What is the probability more than 9 of the problems can be resolved today? (Round your answer to 4 decimal places.)

P( x >9) =P( x=10)+P( x=11)+P(x=12)+P(x=13)+P(x=14)

= 0.2219+0.1715+0.0911+0.0298+0.0045

=0.5187

Binomial Probabilities Tablefor p=0.68
	X	P(X)
	0	0.0000
	1	0.0000
	2	0.0000
	3	0.0004
	4	0.0024
	5	0.0102
	6	0.0326
	7	0.0793
	8	0.1474
	9	0.2088
	10	0.2219
	11	0.1715
	12	0.0911
	13	0.0298
	14	0.0045