3. (5 points) - One of the Beef-O-Brady's restaurants in the Lakeland area has been facing long customers waiting time on weekends, so the General Manager decided to implement a Waiting-Tracking App (WTA) System on 09/25/2022, which requires a cell phone APP. Basically, the customer check-in online on their cell phone APP and he/she will be notified within 1520 minutes that their table is ready. The table below presents the daily waiting time average in the 10 days preceding the implementation of the WTA System and 10 days after the implementation: By using the 10 data points provided before and after the implementation of the WTA System, calculate: a. ( 2 points) - The average waiting time during the 10-day period before and after the implementation of the APP. Based on average waiting time, was the implementation successful? Discuss the results and calculate the reduction in average waiting time in %. b. ( 2 points) - The following measures of variability: standard deviation, coefficient of variation and range for waiting time during the 10-day period before and after the implementation of the APP. Based on these three measures of variability, is the new process performing better? Discuss the results. c. ( 1 points) Plot a scatter diagram containing the data points available for waiting time from 09/15 to 10/04. Once the new APP was implemented on 09/25 and through the following 10 days, what can you observe about the trends in waiting time? 4. (10 points) - The General Manager from Trust Auditing Company already studied in Problem #1 provided additional information about the sample of 20 customers, by informing which customer is a "For Profit Organization" as shown on the table below: Guidance: This problem covering Conditional Probability is very similar to the example presented on your textbook on page 164. In problem #1, you have already calculated the average time it takes these 20 customers to complete the audit (before the elimination of the outlier), so you will be able to identify which customer audits are executed under the average time and which customer audits are executed above the average time. Let's define the following events: A: event that a customer audit is executed above the average time (it takes longer than the average time to complete audit) B: event that a customer audit is executed below the average time (it takes shorter than the average time to complete audit) P: event that a customer is a For Profit Organization N : event that a customer is a Not-for Profit Organization a. ( 2 points) - Create the following crosstabulation of customer audit execution time and if customer is a For Profit Organization or Not: ATTENTION: In order to get the points, show all steps of the calculations of the Joint Probabilities c. ( 2 points) - Calculate the probability that the customer audit is executed above the average time (event A) given that the customer is a For Profit Organization (event P). d. ( 2 points) - Calculate the probability that the customer is a For Profit Organization (event P) given that the customer audit is executed above the average time (event A). e. ( 2 points) - Calculate the probability that the customer audit is executed below the average time (event B) given that the customer is Not for Profit Organization (event N). 3. (5 points) - One of the Beef-O-Brady's restaurants in the Lakeland area has been facing long customers waiting time on weekends, so the General Manager decided to implement a Waiting-Tracking App (WTA) System on 09/25/2022, which requires a cell phone APP. Basically, the customer check-in online on their cell phone APP and he/she will be notified within 1520 minutes that their table is ready. The table below presents the daily waiting time average in the 10 days preceding the implementation of the WTA System and 10 days after the implementation: By using the 10 data points provided before and after the implementation of the WTA System, calculate: a. ( 2 points) - The average waiting time during the 10-day period before and after the implementation of the APP. Based on average waiting time, was the implementation successful? Discuss the results and calculate the reduction in average waiting time in %. b. ( 2 points) - The following measures of variability: standard deviation, coefficient of variation and range for waiting time during the 10-day period before and after the implementation of the APP. Based on these three measures of variability, is the new process performing better? Discuss the results. c. ( 1 points) Plot a scatter diagram containing the data points available for waiting time from 09/15 to 10/04. Once the new APP was implemented on 09/25 and through the following 10 days, what can you observe about the trends in waiting time? 4. (10 points) - The General Manager from Trust Auditing Company already studied in Problem #1 provided additional information about the sample of 20 customers, by informing which customer is a "For Profit Organization" as shown on the table below: Guidance: This problem covering Conditional Probability is very similar to the example presented on your textbook on page 164. In problem #1, you have already calculated the average time it takes these 20 customers to complete the audit (before the elimination of the outlier), so you will be able to identify which customer audits are executed under the average time and which customer audits are executed above the average time. Let's define the following events: A: event that a customer audit is executed above the average time (it takes longer than the average time to complete audit) B: event that a customer audit is executed below the average time (it takes shorter than the average time to complete audit) P: event that a customer is a For Profit Organization N : event that a customer is a Not-for Profit Organization a. ( 2 points) - Create the following crosstabulation of customer audit execution time and if customer is a For Profit Organization or Not: ATTENTION: In order to get the points, show all steps of the calculations of the Joint Probabilities c. ( 2 points) - Calculate the probability that the customer audit is executed above the average time (event A) given that the customer is a For Profit Organization (event P). d. ( 2 points) - Calculate the probability that the customer is a For Profit Organization (event P) given that the customer audit is executed above the average time (event A). e. ( 2 points) - Calculate the probability that the customer audit is executed below the average time (event B) given that the customer is Not for Profit Organization (event N)