Question

Using the Quality Summary and Call Center Data, provide a summary report for the vice president including the following information in an essay with a minimum of 500 words:

1. Based on the probability of an error provided in the quality summary under call quality using a sample size of 15, predict the probability of both < 2 errors or >= 5 errors using the correct discrete probability distribution. Assume calls are either correct or incorrect.
2. Using the call time mean and standard deviation from the quality sample, find the probability of a call time < 7min, between 7 and 9 min, and > 9 min.
3. Calculate and evaluate the 95% confidence interval for the mean from the call time data.

A15 B C D F F G H J 1 Overall Incoming Calls by Type 2 Check coverage of policy 3 Check status of claim Call Quality Call Errors Frequency Frequency Frequency Correct Incorrect coverage quote (COV) Incorrect capture of claim (CLM) Did not transfer to "Save a Policy" (SAV) Incorrect claim status provided (STAT) 25625 850 54 Incorrect 150 22654 42 4 Update address 5 File a claim 6 Update information on claim 7 Update Policy 8 Cancel Policy 18723 32 13499 22 6200 5126 3842 E27 E F Q K Call Time Reason L D lTie C N Call Time Reason Call Call Time Reason Call Time Reason Call Time Reason Shift Shift Shift Shift Shift Shift Shift Са Reason Reason 9.50 CLM 18.00 COV 12.00 STAT 6.75 STAT PM 6.50 STAT AM AM AM PM 16.00 CLM PM PM 9.25 STAT 6.50 STAT AM 10.00 COV AM 6.00 COV PM 12.50 CLM PM 16.50 CLM PM 6.75 STAT 9.25 CLM AM AM AM 10.00 COV AM 9.00 COV 12.50 CLM PM 17.00 COV PM 7.25 SAV PM 6.50 STAT PM PM 9.25 COV 6.50 STAT AM 10.00 COV AM 9.50 COV PM 12.50 CLM PM 17.50 COV PM 7.25 SAV AM 9.25 SAV AM 7.00 SAV AM 10.00 COV AM 10.00 SAV PM 12.50 CLM PM 18.00 SAV PM 7.75 SAV PM 10.25 STAT PM 6 7 7.00 COv AM 10.00 COV AM 10.50 COv PM 13.00 CLM PM 18.00 SAV PM 7,75 SAV AM 10.25 COV AM 8 7.00 COV AM 10.50 CLM AM 10.50 COV PM 13.00 CLM PM 18,00 COV PM 7,75 CLM PM 10.25 SAV PM 7,00 COV AM 10.50 CLM AM 11.00 CLM PM 13.50 CLM PM 18.50 SAV PM 7,75 CLM AM 10.75 COV AM 10 7.00 COV AM 10.50 CLM AM 11.00 CLM PM 13.50 CLM PM 19.00 COV PM 8.25 CLM PM 10.75 COV PM 11 8.00 COV AM. 10.50 CLM AM 11.00 COV PM 14.00 COV PM 19.50 COV PM 8.25 CLM AM 10.75 SAV AM 12 8.00 COV AM 10.50 CLM AM 11.00 COV PM 14.00 SAV PM 19.50 COV PM 8.25 CLM PM 10.75 COV PM 11.50 CO 13 8.50 SAV AM 10.50 CLM AM PM 14.00 COV PM 5.25 STAT AM 8.75 CLM AM 11.25 COV AM 8.75 5.25 STAI PM 10 50 SAV 9.00 SAV ... 16 9,00 SA AM 11,50 SAV AM PM PM 5.25 ST PM 8.75 SAV PM 11.75 COV PM 17 9.00 COV AM 11.50 SAV AM 12.00 COV PM 14.50 COV PM 5.75 STAT AM 8.75 SAV AM 12.25 COV AM 5.7 9 50 COv 15. 00 CLM .. ... 12.00 CLM AM PM TAT 9.25 SAV AM 14 75 SAV AM 20 9.50 CLM AM PM PM 9.25 CLM 12.00 CLM AM 12.00 STAT PM 15.00 CLM 5.75 STAT PM 15.25 SAV PM 21 12.00 CLM AM 12.00 STAT PM 15.50 CLM PM 5.75 STAT AM 9.25 COV AM 15.75 SAV AM 22 16.75 SAV PM

Answer 1

The report is as follows:

The report relates to the quality of the calls taken at a call center. The data relates to a total of 1000 calls. Thus the sample size is 1000 calls, There quality and error types have been recorded. Out of the 1000 calls , 850 calls are considered to be correct and error free. Remaining 150 of the calls are considered to be incorrect. Then there has been an analysis about the types of calls. Like what do the calls come on, what problem needs to be addressed on the call. It has been recorded that there 26.79% of the calls that relate to the coverage of the policy. 23.68% of the calls relate to the status of the claim. There are some calls that come to get their address updated. The percent of such calls is 19.57%. There are 14.11% of the calls that come in order to file a claim. Very few calls come to update the information of the claim. The percent of such calls is 6.48%. 5.36% of the calls come to update the policy , and 4.02% of the calls come to cancel the policy for them. These are various reasons of the incoming calls. We can observe than the maximum percent relates to the coverage of the policy , whereas the least number of calls relate to the cancellation of the policy.

The incoming calls turn to be incorrect due to various reasons. The categories are as follows:

Incorrect coverage
Incorrect capture of the claim
Call not transferred to save the policy
Incorrect status of the claim provided
Majority errors relate to incorrect coverage provided to the customer. 36% of the incorrect calls are due to the error of incorrect coverage provided to the customer

28% of the incorrect calls are due to the incorrect capturing of the claim ,. This means that the claim is recorded or understood and mentioned incorrectly. This leads to no solution of the exact claim of the customer.

21% of the calls are considered to be incorrect if they are not transferred to the higher level , in order to give a try to save the policy from being cancelled. This is an important aspect , as this leads to loss of customers.

Last and the least number of incorrect calls relate to providing wrong status of the claim to the customers, this creates wrong expectations among the customers and results in dissatisfied customers. The percent of such calls is 15% of the total incorrect calls.

Thus like this we get to know what the incoming calls relate to and how it can be addressed better, plus we also get to know the quality rate of the calls. On indepth analysis we were able to find the errors made on call and this helps us to know on which areas do we need to work upon and ensure that the call quality improves in future. We can find ways to make sure that each type of error is addressed properly and action must be taken on providing incorrect information to the customer..

.

Answer to question number 1)

if there are n = 15 calls

we need to find the probability of 2 or less errors

P (error) = 0.15

.

Then we make use of binomial probability formula:

P(x < = 2) = P(x=0) + P(x=1) + P(x=2)

P(x=0) = 15C0 0.15^0 0.85^15 = 0.08735

P(x=1) = 15C1 0.15^1 0.85^14 = 0.23123

P(x=2) = 15C2 0.15^2 0.85^13 = 0.28564

.

P(X<=2) = 0.28564 + 0.23123 + 0.08735

P(x < = 2) = 0.604225

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