any and all questions are beneficial

Variability, Chapter 8 (Max 50 points), Problem Environment: My-law.com is a recent start-up trying to cater to customers in search of legal services who are intimidated by the idea of talking to a lawyer or simply too lazy to enter a law office. Unlike traditional law firms, My-law.com allows for extensive interaction between lawyers and their customers via telephone and the Internet. This process is used in the upfront part of the customer interaction, largely consisting of answering some basic customer questions prior to entering a formal relationship. In order to allow customers to interact with the firm's lawyers, customers are encouraged to send emails to mylawyerr@My-law.com. From there, the incoming emails are distributed to a lawyer who is currently "on call." Given the broad-lwa skills of the lawyers, each lawyer can respond to each incoming request. E-mails arrive at a rate of 20 emails per hour (coefficient of variation for the arrivals is 1.2). At each moment in time, there are exactly two lawyers "on call," that is, sitting at their desk waiting for incoming emails or responding to emails. It takes a lawyer, on average, 5 minutes to write the response email; only one lawyer works on a response and both lawyers have identical capabilities. The standard deviation of this time is 4 minutes. 1. (*7.5 points) This basic variability question is not related to the My-law.com environment. Consider the following set of inter-output (inter-departure) times from a station, collected by observations over an interval of about an hour: 5.1, 4.9, 5.0, 5.0, 5.2, 5.1, 4.8, 4.9, 5.0, 5.0. Compute the coefficient of variation for this sample. Do you have any concerns about this data set and how would you address your concern? If you have no concerns, explain why your lack of concern is reasonable. 2. (5 points) What is the numerical value of the average inter-arrival time of customer emails (the time between two consecutive arrivals)? Be specific with the time unit. 3. (5 points) What is the numerical value of the coefficient of variation (CV) for the service time = the time spent on actually writing the email by the lawyer? 4. (*7.5 points) When not responding to emails, the lawyer on call is encouraged to actively pursue cases that potentially could lead to large settlements. How much time in a 10-hour day (from 8 AM to 6 PM) can a Mylaw.com lawyer dedicate to this activity of working on a settlement (assume the lawyer can instantly switch between emails and work on a settlement)? 5. (10 points) Compute the average time a customer must wait for the response to his/her email, ignoring any transmission times. Note: This includes the time it takes the lawyer to start writing the email (i.e., queueing time for the customer) and the actual writing time. 6. ( 5 points) On average how many emails are there in the system waiting to be responded to? 7. (*10 points) Given the data values in this problem instance, what data inputs would you seek to change first to improve the TH, CT performance of the system? Explain why you picked which data inputs