Question
In: Statistics and Probability
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions...
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute. Also assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customers per minute. Determine the probabilities of 0, 1, 2, and 3 customers in the system. Round your answers to 4 decimal places. n P(n) 0 1 2 3 What is the probability that more than three customers will be in the drive-up teller system at the same time? Round your answer to 4 decimal places. P (n > 3) =
Solutions
orchestra answered 2 years agoRelated Solutions
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions...
Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 30 customers
per hour or 0.5 customers per minute.
(a)
What is the mean or expected number of customers that will
arrive in a four-minute period?
(b)
Assume that the Poisson probability distribution can be used to
describe the arrival process....
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions...
Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 24 customers
per hour or 0.4 customers per minute. In the same bank waiting line
system, assume that the service times for the drive-up teller
follow an exponential probability distribution with a service rate
of 36 customers per hour, or 0.6...
Will Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars
Will Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with the mean of 2 customers every 5 minutes. Assume that a Poisson probability distribution can be used to describe the arrival process.
a. Compute the probability that exactly 1 customer will arrive in a 5-minute period
b. Compute the probability that exactly 3 customers...
A Security Pacific Bank branch has opened up a drive through teller window. There is a...
A Security Pacific Bank branch has opened up a drive through teller
window. There is a single service lane, and customers in their cars
line up in a single line to complete bank transactions. The average
time for each transaction to go through the teller window is
exactly four minutes. Throughout the day, customers arrive
independently and largely at random at an average rate of ten
customers per hour.
1) What is the probability that there are exactly 3 cars...
The La Puerta Bank of Stockholm City has one outside drive-up teller. It takes the teller...
The La Puerta Bank of Stockholm City has one outside drive-up
teller. It takes the teller an average of 4 minutes to serve a bank
customer. Customers arrive at the drive-up window at a rate of 12
per hour. The bank operations officer is currently analyzing the
possibility of adding a second drive-up window, at an annual cost
of Php 1,000,000. It is assumed that arriving cars would be equally
divided between both windows. The operations officer estimates that
each...
The drive-up window at a local bank is searching for ways to improve service. One of...
The drive-up window at a local bank is searching for ways to
improve service. One of the tellers has decided to keep a control
chart for the service time in minutes for the first four customers
driving up to her window each hour for a three-day period. The
results for her data collection appear below:
Customer
TIME
9 am
10 am
11 am
12
1 pm
2 pm
3 pm
4 pm
1
1.4
3.8
3.6
4.3
4.0
1.3
0.9...
Customers arrive at the drive-up window of a fast-food restaurant at a rate of 2 per...
Customers arrive at the drive-up window of a fast-food
restaurant at a rate of 2 per minute during the lunch hour
What is the probability that the next customer will arrive
within 1 minute?
What is the probability that the next customer will arrive
after 0.5 minutes?
What is the probability that the next customer will arrive
between 45 seconds and 1.5 minutes?
Customers arrive at a drive-up window of a fast-food restaurant at a rate of 3 per...
Customers arrive at a drive-up window of a fast-food
restaurant at a rate of 3 per minute during lunch hour.
a. What is the probability that the next customer will arrive
within 1 minute?
b. What is the probability that the next customer will arrive
within 3 minutes?
c. During the dinner time period, the arrival rate is 2 per
minute. What are your answers to a and b for this period?
Round to four decimal places as needed.
Customers arrive at a drive-up window of a fast-food restaurant at a rate of 2 per...
Customers arrive at a drive-up window of a fast-food
restaurant at a rate of 2 per minute during lunch
hour.
a. What is the probability that the next customer will
arrive within 2 minutes?
b. What is the probability that the next customer will
arrive within 3 minutes?
c. During the dinner time period, the arrival rate is 1
per minute. What are your answers to a and b for this
period?
Frost Bank finds that 24 customers arrive at the single drive-through per hour. The teller is able to complete 32 transactions per hour. Assume M/M/1 operating characteristics.
Frost Bank finds that 24 customers arrive at the single drive-through per hour. The teller is able to complete 32 transactions per hour. Assume M/M/1 operating characteristics.
1. What is the average time a customer spends waiting?
2. What is the probability that the system is idle?
3. What is the probability that there are more than 4 customers in line?
4. What is the average number of customers in line?
5. How long does the average customer spend...
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