Unit 6 Assignment

Unit 6 Assignment

Solve Problems 6 and 8. Please be sure to show ALL your work.

Problem 6

6. Trucks are required to pass through a weighing station so that they can be checked for weight viola- tions. Trucks arrive at the station at the rate of 40 an hour between 7:00 p.m. and 9:00 p.m. Cur- rently two inspectors are on duty during those hours, each of whom can inspect 25 trucks an hour.

1. How many trucks would you expect to see at the weighing station, including those being inspected?
2. If a truck was just arriving at the station, about how many minutes could the driver expect to be at the station?
3. What is the probability that both inspectors would be busy at the same time?
4. How many minutes, on average, would a truck that is not immediately inspected have to wait?
5. What condition would exist if there was only one inspector?
6. What is the maximum line length for a probability of.

Problem 8

The parts department of a large automobile dealership has a counter used exclusively for mechan- ics’ requests for parts. The time between requests can be modeled by a negative exponential distri- bution that has a mean of five minutes. A clerk can handle requests at a rate of 15 per hour, and this can be modeled by a Poisson distribution that has a mean of 15. Suppose there are two clerks at the counter.

1. On average, how many mechanics would be at the counter, including those being served?
2. What is the probability that a mechanic would have to wait for service?
3. If a mechanic has to wait, how long would the average wait be?
4. What percentage of time are the clerks idle?
5. If clerks represent a cost of $20 per hour and mechanics a cost of $30 per hour, what number of clerks would be optimal in terms of minimizing total co