Question

An airline operates a call center to handle customer questions and complaints. The airline monitors a sample of calls to help ensure that the service being provided is of high quality. Ten random samples of 100 calls each were monitored under normal conditions. The center can be thought of as being in control when these 10 samples were taken. The number of cats in each comple not resulting in a satisfactory resolution for the customer is as follows. 32 33 454 4 4 (a) What is an estimate of the proportion of calls tot resulting in a satisfactory outcome for the customer when the centers in control? (b) Construct the upper and lower limits for a chart for the manufacturing process, assuming each sample has 100 calls (Round your answers to four decima proces) UCL - Li c) with the results of part (). what conclusion should be made a sample of 100 as 11 calls het resulting in sectory resetion for the customer Sincep the control the process is for the same (0) Compute the poet and lower limits for the heart and your answers to the decis UL- LCL e) with the res of part (d), what conclusion made a sample of 100 cm 11 oresong is a bisectory condusion for the customer? Since the number of call not resulting in a story conclusion is the control the process for the same

Answer 1

Answer:

a)

Given,

No. of samples k = 10

sample n = 100

Estimate of population p = x/nk = (4 + 4 + 3 + 2 + 3+ 3 + 4 + 5 + 4 + 8)/(100*10)

= 0.04

b)

Standard deviation = sqrt(pq/n) = sqrt(0.04(1-0.04)/100) = 0.0196

UCL = p + 3*sd = 0.04 + 3*0.0196 = 0.0988- 0.0188

LCL = p - 3*sd = 0.04 - 3*0.0196 = - 0.0188

Here limits can't be negative, so LCL = 0

c)

Here the sample proportion p = 0.11 is out of control limit, the process is out of control.

d)

p = 0.04 , n = 100

UCL = np + 3*sqrt(npq) = 100*0.04 + 3*sqrt(100*0.04(1-0.04)) = 9.88

LCL = np - 3*sqrt(npq) = 100*0.04 - 3*sqrt(100*0.04(1-0.04)) = - 1.88

Here limits can't be negative, so LCL = 0

e)

The process is out of control since 11 > UCL