A call center is examining its data regarding the complaints of its callers. Two complaint areas are identified: customers who complain due to the wait time to talk to an agent, and customers who complain due to inexperienced agents. Each data set consists of number of complaints per week. The Excel file Assignment3_Problem1_Data includes the complaint data for the last year for these two categories.

1. What is the distribution of weekly complaints in each category? Identify the name of the distribution and its mean and standard deviation. Fit a continuous distribution to the data and use the K-S test as goodness-of-fit criteria.
2. Are the two categories of weekly complaints correlated to each other? If yes, describe their correlation.

Set up a simulation that calculates the total complaints by week. In your simulation, there will be two input variables – one for weekly complaints due to the wait time to talk to an agent and one for the weekly complaints due to inexperienced agents. Use the fitted distributions that you identified in (a). If there is a correlation between the complaint types, include it in your model. Using your simulation model, answer the following questions.

1. What is the mean and standard deviation of the total complaints by week?
2. What is the 95% confidence interval for the mean complaints by week? Interpret this interval.
3. What is the probability that the total complaints in a week will be less than 600?
4. What is the probability that the total complaints in a week will be bigger than 2600?

Now, re-run the simulation by ignoring the correlation among the complaint types and re-answer
questions (c)- (f) above. How would your answers to those questions change? What is the impact of
ignoring correlation in this setting?