Over the years, Detective Columbo, of the Fayetteville Police Department, has had phenomenal success in solving every single crime case. It is only a matter of time before any case is solved. Columbo admits that the time per case is "totally random" but, on average, each investigation will take about a week and a half. Crimes in peaceful Fayetteville are not very common. They occur randomly at the rate of one crime per month (4 weeks). Detective Columbo is asking for an assistant to share the heavy workload. Analyze Columbo's claim, particularly from the standpoint of the following points: a) The average number of cases awaiting investigation. b) The percentage of time the detective remains busy. c) The average time needed to solve a case.