Exercise 1 Improving customer service A bank branch located in a commercial dist

ID: 3216400 • Letter: E

Question

Exercise 1 Improving customer service A bank branch located in a commercial district of a city has developed a process to improve customer service during the noon to 1 pm lunch period. The waiting time in minutes of all customers during this hour is recorded over a period of one week. The waiting time is defined as the time the customer enters the line to when he or she reaches the teller wndow.Arandom smple of 5 customers s setdthe resutsarie olos 4.21 5.55 0.5 5.13 4.772.34 3.54 3.2 4.5 6.1 0.38 5.12 6.46 12.19 3.79 Use an appropriate technique to summarise the data and answer following questions.

Explanation / Answer

Solution

Let xi = waiting time of the ith sample customer.

Ex 1 Part (g)

Shape of waiting time data

The Waiting Time data is summarized below:

Waiting Time

Tally Marks

Frequency

0.38

0.5

0.5 – 2.25

2.25 – 4.25

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4.25 – 6.5

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6.5 – 12.0

12.19

To read the above frequency distribution,

0.38, 0.5 and 12.19 do not fall into the main stream. Of the remaining 12 values, 4 lie to the left of 4.25 while 8, i.e., double the number, fall to the right. Thus, the waiting time data is to be considered positively skewed (right tailed). ANSWER

Ex 1 Part (h)

Unusual Waiting Time

Clearly, 0.38, 0.5 and 12.19 are unusual and outliers. ANSWER

Ex 1 Part (i)

Unusual Waiting Time - Treatment

The outliers, 0.38, 0.5 and 12.19 are to be kept out of the statistical analysis since these values do not represent the main stream and hence if included would lead erroneous conclusions which may not reflect the reality. ANSWER

Ex 2

Interpretation

Summary Statistics

Based on the 12 values. i.e., ignoring the three outliers, the analysis shows:

Average Waiting Time = 4.56 and Standard Deviation = 1.21 ANSWER

Ex 3

Statistical Thinking

A standard deviation of 1.21 for an average of 4.56 is indeed high. This, implies that there is high inconsistency in the waiting time which in turn is a reflection of the service efficiency. Thus, the service efficiency needs to be made more consistent by streamlining the operations. A xbar-R Control Chart would come in handy to detect the aberrations and bring stability.

ANSWER