Chapter D additional ALL ANSWERS 100% CORRECT FALL-2021 SOLUTION GUARANTEED GRADE A+

Due to a recent increase in business, a law firm secretary must now word-process an average of 20 letters a day (assume a Poisson distribution). It takes him approximately 20 minutes to type each letter (assume an exponential distribution). Assuming the secretary works 8 hours a day: a) What is the secretary’s utilization rate? a 0.833 b) What is the average waiting time before the secretary word-processes a letter? a 0.2083 12 ½ mins c) What is the average number of letters waiting to be done? a 4.17 letters d) What is the probability that the secretary has more than 5 letters to do? a 33% ; (1-0.6651) D.27 At the start of football season, the ticket office gets very busy the day before the first game. Customers arrive at the rate of four every 10 minutes, and the average time to transact business is 2 minutes. a) What is the average number of people in line? a 3.2 people b) What is the average time that a person will spend at the ticket office? a 0.167 10 mins c) What proportion of time is the server busy? a 80% D.28 Bryce Dodson’s Car Wash is open 6 days a week, but its busiest day is always Saturday. From historical data, Bryce estimates that dirty cars arrive at the rate of 20 per hour all day Saturday. With a full crew working the hand-wash line, he figures that cars can be cleaned at the rate of one every 2 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the following: a) The average number of cars in line. a 1.3 cars b) The average time that a car waits before it is washed. a .0667 4 mins c) The average time that a car spends in the service system. a .1 6 mins d) The utilization rate of the car wash. a 67% e) The probability that no cars are in the system. a 33% Additional Homework Problemsf) Bryce is thinking of switching to an all-automated car wash that uses no crew. The equipment under consideration washes one car every minute at a constant rate. How will your answers to parts (a) through (e) change with the new system? a .08