Customers arrive at a local grocery store at an average rate of 2 per minute. (a)...

Customers arrive at a local grocery store at an average rate of 2 per minute.

(a) What is the chance that no customer will arrive at the store during a given two minute period?

(b) Since it is a “Double Coupon” day at the store, approximately 70% of the customers coming to the store carry coupons. What is the probability that during a given two-minute period there are exactly four (4) customers with coupons and one (1) without coupons?

(c) Divide one given hour into 30 two-minute periods. Suppose that the numbers of customers arriving at the store during those periods are independent of each other. Denote by X the number of the periods during which exactly 5 customers arrive at the store and 4 of them carry coupons. What is the probability that X is at least 2?

(d) What is the probability that exact 4 customers coming to the store during a given two-minute period carry coupons?

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the...

Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places. Part a) What is the probability that exactly two customers arrive in a minute? Part b) Find the probability that more than three customers arrive in a two-minute period. Part c) What is the probability that at least seven customers arrive in three minutes, given...

Customers arrive at a local ATM at an average rate of 14 per hour. Assume the...

Customers arrive at a local ATM at an average rate of 14 per hour. Assume the time between arrivals follows the exponential probability distribution. Determine the probability that the next customer will arrive in the following time frames. a) What is the probability that the next customer will arrive within the next 2 minutes? b) What is the probability that the next customer will arrive in more than 15 minutes? c) What is the probability that the next customer will...

1. A grocery store counts the number of customers who arrive during an hour. The average...

1. A grocery store counts the number of customers who arrive during an hour. The average over a year is 29 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 2 minute period. 2. Label each as one of the following...

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 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...

(Operations Management) The grocery store gets an average of 50 customers per shift. The manager wants...

(Operations Management) The grocery store gets an average of 50 customers per shift. The manager wants to calculate whether he should hire one, two, three, or four salespeople. The average waiting times will be seven minutes with one salesperson, four minutes with two salespeople, three minutes with three salespeople, and two minutes with four salespeople. He has estimated the cost per minute that customers wait at $1. The cost per salesperson per shift (including fringe benefits) is $70. Analyze to...

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...

Your local grocery store claims that on average their fresh caught salmon will weigh 2 pounds....

Your local grocery store claims that on average their fresh caught salmon will weigh 2 pounds. You want to test to see if their claim is correct so you gather a simple random sample of 45 packages of their fresh caught salmon, weigh each package, and find that the average weight of these packages is 1.76 pounds. Based on years of data, the grocery store determined that the standard deviation ? = 0.08 pounds. What is the probability of obtaining...

QUESTION 19 Jean guesses that 35% of customers at a local grocery store will choose the...

QUESTION 19 Jean guesses that 35% of customers at a local grocery store will choose the self check-out lane over the full service cashier lane. Throughout one day, she gathers data by observing 228 customers in the store. She finds that 74 of them choose the self check-out lane. Was her guess reasonable? Assume 95% confidence. (Hint: You may use either a confidence interval or hypothesis test to help you answer this question.) A. Yes, her guess was reasonable. B....

Customers enter the camera department of a store at an average rate of five per hour....

Customers enter the camera department of a store at an average rate of five per hour. The department is staffed by one employee, who takes an average of 8.0 minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation. (Use the Excel spreadsheet Queue Models.) a-1. As a casual observer, how many people would you expect to see in the camera department (excluding the clerk)? (Round your answer to 2 decimal places.) a-2....

Subjects