Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a ty
ID: 349501 • Letter: N
Question
Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 12 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is 3 minutes. It is assumed that service times may be described by the negative exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teler is us a) The average time in the line minutes (round your response to two decimal places) b) The average number in the line customers (round your response to two decimal places). c) The average time in the systemminutes (round your response to two decimal places d) The average number in the system customers (round your response to two decimal places) e The probability that the bank is empty· round your response to two decimal places )CEO Benjamin Neve is considering adding a second teller (who would work at the same rate as the first) to reduce the waiting time for customers. He assumes th this will cut the waiting time in half if a second teller is added, the average time a customer spends in the queue minutes (round your response to two decimal places). If a second teller is added, the average number of customers in the queue customors (round your response to four decimal places). If a second toller is added, the average tirne a customer spends in the system . minutes (round your response to two decimal places). lf a second teller is added, the average number of customers in the system: customers round your response to three dec mal places I ).Explanation / Answer
PLEASE FIND ANSWERS TO FIRST 5 QUESTIONS :
Given are following data :
Compacted Lift thickness = g inches = 0.5 feet
Roller width = 10 feet
Distance covered in an hour = 5 mph = 5 x 5280 feet = 26400 feet
Total compaction in an hour
= Compacted lift thickness x Roller width x Distance covered = 0.5 x 10 x 26400 = 132,000 cubic feet
Effective compaction considering 0.65 efficiency = 0.65 x 132,000 = 85800 cubic feet = 85800/ 27 cubic yard = 3177.78 ( rounded to 2 decimal places )
PRODUCTION IN COMPACTED CY PER HOUR = 3177.78 CY
We assume arrival rate follows Poisson distribution
Given are following data :
Arrival rate = a = 12 customers / hour
Service rate ( 3 minutes per transaction ) = S = 60 /3 = 20 customers/ hour
Answer to question a:
The average time in the line = a / S x ( S – a ) = 12/20 x ( 20 -12 ) = 12 / 20x 8 = 12/160 hour = 720/160 minutes= 4.5 minutes
THE AVERAGE TIME IN THE LINE = 4.5 MINUTES
Answer to question b :
The average number in the line
= Arrival rate x The average time in the line
= 12 / hour x 12/160 hour
= 144/160
= 12/15
= 0.8
AVERAGE NUMBER IN THE LINE = 0.80
Answer to question c :
Average time in the system = a/ S x ( S – a ) + 1/S
= 12/20 x ( 20 – 12 ) + 1/20 hour
=12/160 + 1/20 hour
= ( 12 + 8)/160 hour
= 20/160 hour
= 1200/160 minutes
= 7.5 minutes
AVERAGE TIME IN THE SYSTEM = 7.5 MINUTES
Answer to question d :
Average number in the system
= Average time in the system x Arrival rate
= 20/160 hour x 12 customers/ hour
= ( 20 x 12)/160
= 1.5
AVERAGE NUMBER IN THE SYSTEM = 1.5 CUSTOMERS
Answer to question e :
Probability that the bank is empty = 1 – a/s = 1 – 12 /20 = 1 – 0.6 = 0.4
PROBABILITY THAT A BANK IS EMPTY = 0.4
PRODUCTION IN COMPACTED CY PER HOUR = 3177.78 CY
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.