3. 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 the average, each investigation will take about a week and half. Crimes in peaceful Fayetteville are not very common. They occur randomly at the rate of one crime per (four-week)

month. Detective Columbo is asking for an assistant to share the heavy work load. 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.