Answer Happy

1. In order to study the length of time after billing for customers to settle the payments, a manager of a virtual bank took a random sample of 100 credit card invoices. A frequency table for the data on payment time, i.e., the number of days between the invoice date and the payment receipt date, was constructed as below. Payment time (in days) Number of invoices 0 - 9 7 10 - 19 20 20 - 29 48 30 - 39 19 40 - 59 6 (a) Calculate the mean, mode, standard deviation and interquartile range. [8 marks] (b) Calculate the coefficient of skewness using results in (a) and interpret your result briefly. [2 marks] (c) In order to encourage early payment, the following scheme is introduced: • For payments made before the mean payment time, the company refunds the customers for each invoice $50 a day for the number of days before the mean payment time. • For payments made after the mean payment time, the company charges the customers for each invoice $100 a day for the number of days after the mean payment time. How much on average will the bank receive/spend per invoice on the above 100 invoices under this scheme? [6 marks] (d) Develop a 99% confidence interval for the mean payment time of all credit card invoices. (4 marks