Question

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 80% of the cases. Suppose the 15 cases reported today are representative of all complaints.

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

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

2. What is the probability 6 of the problems can be resolved today? (Round your answer to 4 decimal places.)

3. What is the probability 6 or 7 of the problems can be resolved today? (Round your answer to 4 decimal places.)

4. What is the probability more than 10 of the problems can be resolved today? (Round your answer to 4 decimal places.)

Answer 1

Probability of solving the problems same day = 80% = 0.80

n= 15

(a) No of problems expected to be solved today = np = 15* 0.80 = 12

variance = n * p* (1-p) = 15 * 0.80* 0.20 = 2.4

standard deviation = sqrt (2.4). = 1.5492

mean = 12 and sd = 1.5492

(b) P(x=6)

P(x= 6) = 0.0007

(c) P(x=6) or P(x=7) = P(x=6) + P(x=7)

P(x = 6 or 7 ) = 0.0007 + 0.0035 = 0.0041

(d) P(x >10) = P(11) + P(12) + P(13) +P(14) +P(15)

Using the binomial formula :

P(x >10) = 0.18760417148928 + 0.25013889531904 + 0.23089744183296 + 0.13194139533312 + 0.035184372088832

P(x >10) = 0.83576627606323

P(x >10) = 0.8358