Question

A customer plans to checkout at a grocery store but finds all 5 cashiers busy serving...

A customer plans to checkout at a grocery store but finds all 5 cashiers busy serving other customers. There are no other customers when this person arrives, and they will be served as soon as someone finishes. All customer arrival and service times are independent and exponentially distributed.

a) What is the probability that this customer will not be the last customer to depart?

b) If the average service time per cashier is 4 minutes, what is the average time this customer will spend in the store?

c) If the average arrival rate is 3 customers/minute, on average how many customers will be in the system?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

ANSWER::

a) Probability that not last to depart is 5/6.
As any of the customers can leave last but not him, this is question of conditional probability.

b) The average time will be 8 minutes by this customer. As average time has to be calculated it will time cashier takes with this customer and the other customer.

c) If service time is 3 minutes, it is possible that on average at one time 4 people are there on the system.

NOTE:: I HOPE YOUR HAPPY WITH MY ANSWER....***PLEASE SUPPORT ME WITH YOUR RATING...

***PLEASE GIVE ME "LIKE"...ITS VERY IMPORTANT FOR ME NOW....PLEASE SUPPORT ME ....THANK YOU

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A customer plans to checkout at a grocery store but finds all 5 cashiers busy serving...
A customer plans to checkout at a grocery store but finds all 5 cashiers busy serving other customers. There are no other customers when this person arrives, and they will be served as soon as someone finishes. All customer arrival and service times are independent and exponentially distributed. a) What is the probability that this customer will not be the last customer to depart? b) If the average service time per cashier is 4 minutes, what is the average time...
Four cashiers are on duty in a bank where customers may be assumed to arrive independently...
Four cashiers are on duty in a bank where customers may be assumed to arrive independently and at random, at an average rate of 60 per hour. If a cashier is free, then an arriving customer receives immediate attention; otherwise a central queue is formed. The service time for each cashier may be assumed to be exponentially distributed with mean 2 minutes. The traffic intensity  is . Assume that the queue is in equilibrium What is the probability that at any...
Suppose 3 cashiers are working in a store, independently. Time to serve a customer by cashier...
Suppose 3 cashiers are working in a store, independently. Time to serve a customer by cashier i is Ti ∼ exp(λi ). What is the probability that none of the cashiers complete their current service (assuming that all are busy) in the next 2 minutes?
In a grocery store, there is one cashier counter. Customers arrive at the cashier counter according...
In a grocery store, there is one cashier counter. Customers arrive at the cashier counter according to a Poisson process. The arrival rate is 30 customers per hour. The service time is exponentially distributed. The mean service time is 1 minute 30 seconds. 1. What is the expected number of customers waiting in the system. 2. What is the expected waiting time.( unit in minutes) 3. What is the utilization rate (unit in %) of the cashier?
At a fashion retailer, there are three cashiers providing checkout service to customers simultaneously. On average,...
At a fashion retailer, there are three cashiers providing checkout service to customers simultaneously. On average, customers arrive at the checkout area every 6 minutes. The standard deviation of the inter-arrival time is 6 minutes. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 16 minutes. Suppose that customers form a single line. What is the average waiting time in minutes for a customer? Keep 2 decimal places for your answer.
1.1 (M/M/1) model - use the qtsPlus or other software to answer the questions. In a...
1.1 (M/M/1) model - use the qtsPlus or other software to answer the questions. In a grocery store, there is one cashier. Customers arrive at the cashier counter according to a Poisson process. The arrival rate is 18 customers per an hour. Customers are served in order of arrival (FCFS: first come first service). The service time (i.e. the time needed for scanning the items and processing payment) is exponentially distributed. The mean service time is 3 minutes. A) Once...
(M/M/c) model - use the qtsPlus or other software to answer the questions. Now, you decided...
(M/M/c) model - use the qtsPlus or other software to answer the questions. Now, you decided to hire one more cashier, so the store has two cashiers. Customers arrive at the cashier counter according to a Poisson process, which is same as the question 1. The arrival rate is 18 customers per an hour. Customers are served in order of arrival (FCFS: first come first service). The service time (i.e. the time needed for scanning and paying) is exponentially distributed....
A supermarket has three cashiers. The supermarket manager implements a policy that if there are 1...
A supermarket has three cashiers. The supermarket manager implements a policy that if there are 1 to 3 customers in the supermarket, then only one cashier is on duty. If there are 4 to 6 customers in the supermarket then two cashiers will be on duty. The three cashiers will be on duty if there are more than 6 customers in the supermarket. The arrival of customers to the supermarket follows the Poisson process with a rate of 10 people...
Dan's Store has installed a self-service checkout counter, and wishes to understand how this has affected...
Dan's Store has installed a self-service checkout counter, and wishes to understand how this has affected customer service. Shoppers arrive on average the rate of one every other minute (Poisson distribution). Each shopper takes an average of 82 seconds to use the checkout, and that time is exponentially distributed. a. Calculate how long it takes, on average, for a shopper at the self-service counter, including how long they wait in line and how long it takes them to do their...
A grocery store counts the number of customers who arrive during an hour. The average over...
A grocery store counts the number of customers who arrive during an hour. The average over a year is 20 customers per hour. Assume the arrival of customers follows a Poisson distribution. (It usually does.) Find the probability that at least one customer arrives in a particular one minute period. Round your answer to 3 decimals.     Find the probability that at least two customers arrive in a particular 4 minute period. Round your answer to four decimals.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT