Essay: Probability Using the Quality Summary and Call Center Data, provide a sum

Question

Essay: Probability 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 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. Call Data and Summary media%2Fa65%2Fa65f1ff2-2363-48b6-8efc-32 Quality Control Call Quality Frequency Relative Frequency Correct 850 850/1000 = 0.850 Incorrect 150 150/1000 = 0.150 Total 1000 1000/1000 = 1 Overall Incoming Calls by Type Frequency Relative Frequency Check coverage of policy 25625 25625/95669 = 0.2679 Check status of claim 22654 22654/95669 = 0.2368 Update address 18723 18723/95669 = 0.1957 File a claim 13499 13499/95669 = 0.1411 Update Information on claim 6200 6200/95669 = 0.0648 Update Policy 5126 5126/95669 = 0.0536 Cancel Policy 3842 3842/95669 = 0.0402 Total 95669 95669/95669 = 1 Call Errors Frequency Relative Frequency Incorrect coverage quote (COV) 54 54/150 = 0.36 Incorrect capture of claim (CLM) 42 42/150 = 0.28 Did not transfer to "Save a Policy" (SAV) 32 32/150 = 0.21 Incorrect claim status provided (STAT) 22 22/150 = 0.15 Total 150 150/150 = 1

Explanation / Answer

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:

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..

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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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