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 calls each were monitored under normal conditions. The center can be thought of as being in control when these samples were taken. The number of calls in each sample of not resulting in a satisfactory resolution for the customer is as follows:

4 5 3 2 3 3 4 6 4 7

Required:
a. What is an estimate of the proportion of calls not resulting in a satisfactory outcome for the customer when the center is in control?
b. Construct the upper and lower limits for a p chart for the manufacturing process, assuming each sample has 100 calls.

Answer:

A) p = 0.041

B) UCL = 0.1004

LCL = 0

Step-by-step explanation:

We are told that Ten random samples of calls each were monitored .

Thus; n_x = 10

We are told that each sample has 100 calls. Thus; n = 100

A) We are given the number of calls in each sample not resulting in a satisfactory resolution for the customers as;

4 5 3 2 3 3 4 6 4 7

Thus, sum of this is;

Σx = 4 + 5 + 3 + 2 + 3 + 3 + 4 + 6 + 4 + 7

Σx = 41

proportion of calls not resulting in a satisfactory outcome for the customer when the center is in control is given by;

p = Σx/(n_x•n)

p = 41/(10 × 100)

p = 41/1000

p = 0.041

B) let's first find the standard deviation.

It's given by the formula;

σ = √(p(1 - p)/n)

σ = √(0.041(1 - 0.041)/100)

σ = 0.0198

Formula for Upper control limit(UCL) and Lower control limit(LCL) are given as;

UCL = p + 3σ

LCL = p - 3σ

Thus;

UCL = 0.041 + 3(0.0198)

UCL = 0.1004

LCL = 0.041 - 3(0.0198)

LCL = -0.0184

Rule is that when LCL is negative, we adopt LCL = 0.

Thus;

UCL = 0.1004

LCL = 0

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