Customers arrive to the checkout counter of a convenience store according to a Poisson process at...

Customers arrive to the checkout counter of a convenience store according to a Poisson process at a rate of two per minute. Find the mean, variance, and the probability density function of the waiting time between the opening of the counter and the following events:

a. The arrival of the second customer.

b. The arrival of the third customer.

c. What is the probability that the third customer arrives within 6 minutes? You can use a computer if you’d like but you need to write down the integral with all of the numbers plugged in.

Expert Solution

orchestra answered 2 years ago

Customers arrive at a department store according to a Poisson process with an average of 12...

Customers arrive at a department store according to a Poisson process with an average of 12 per hour. a. What is the probability that 3 customers arrive between 12:00pm and 12:15pm? b. What is the probability that 3 customers arrive between 12:00pm and 12:15pm and 6 customers arrive between 12:30pm and 1:00pm? c. What is the probability that 3 customers arrive between 12:00pm and 12:15pm or 6 customers arrive between 12:30pm and 1:00pm? d. What is the probability that a...

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. What is the expected waiting time?

A small auto parts store has a single counter with one employee. Customers arrive at the counter at the rate of 10 per hour according to a Poisson distribution.

A small auto parts store has a single counter with one employee. Customers arrive at the counter at the rate of 10 per hour according to a Poisson distribution. The employee can handle 20 customers per hour and service times are exponentially distributed. Calculate (A) The probability that a customer finds an empty counter in the auto parts store (no customers waiting or being served) (B) The average number of customers waiting in the que at the auto parts store (i.e.,...

Customers arrive at a hair salon according to a Poisson process with an average of 16...

Customers arrive at a hair salon according to a Poisson process with an average of 16 customers per hour. The salon has just one worker due to covied-19 restriction. Therefore, the salon must close whenever the worker leaves. assume that customers who arrive while the salon is closed leave immediately and don’t wait until the worker returns. The salon is closed on weekends. a. What is the probability that at most (less than) four customers arrive in the hour before...

Customers arrive in a certain shop according to an approximate Poisson process on the average of...

Customers arrive in a certain shop according to an approximate Poisson process on the average of two every 6 minutes. (a) Using the Poisson distribution calculate the probability of two or more customers arrive in a 2-minute period. (b) Consider X denote number of customers and X follows binomial distribution with parameters n= 100. Using the binomial distribution calculate the probability oftwo or more customers arrive in a 2-minute period. (c) Let Y denote the waiting time in minutes until...

Customers arrive at an establishment according to a Poisson process of frequency  = 5 per...

Customers arrive at an establishment according to a Poisson process of frequency  = 5 per hour. Since the establishment opens at 9:00 am: a) What is the probability that exactly a client arrived by 9:45 am? b) What is the probability of maximum five clients by 11:45 am?

Customers arrive at a cafe every 2 minutes on average according to a Poisson process. There...

Customers arrive at a cafe every 2 minutes on average according to a Poisson process. There are 2 employees working at the bar providing customer service, i.e., one handling customer orders and another handling payments. It takes an average of 1 minute to complete each order (exponentially distributed). Based on the above: f. What are the service time probability density and cumulative distribution functions? g. What percentage of customer orders will be prepared in exactly 2 minutes? h. What are...

Customers arrive at a service center according to a Poisson process with a mean interarrival time...

Customers arrive at a service center according to a Poisson process with a mean interarrival time of 15 minutes. If two customers were observed to have arrived in the first hour, what is the probability that at least one arrived in the last 10 minutes of that hour?

A small grocery store has a single checkout line. On Saturdays, customers arrive at the checkout...

A small grocery store has a single checkout line. On Saturdays, customers arrive at the checkout on an average of one every 8 minutes. The cashier takes an average of 6 minutes to process a single customer. We assume that the service time is randomly distributed, and the customers arrive randomly. The store's owner believes that the amount of time that a customer has to wait hurts his business; he estimates that waiting time costs him $20 per customer-hour in...

Customers arrive at a service facility according to a Poisson process of rate 5 /hour Let...

Customers arrive at a service facility according to a Poisson process of rate 5 /hour Let N(t) be the number of customers that have arrived up to time t hours). a. What is the probability that there is at least 2 customer walked in 30 mins? b.If there was no customer in the first30 minutes, what is the probability that you have to wait in total of more than 1 hours for the 1 st customer to show up? c.For...

Question