(4) A restaurant based in a city centre monitors the rate at which customers are arriving...
The mean number of customers arriving at a restaurant during a 15-minute period is 8. Find the probability that at least 4 customers will arrive at the restaurant during a 15-minute period.
During lunchtime at a certain fast food restaurant, customers arrive at an average rate of 7 customers every 5 minutes. assume a poisson distribution to find the probability that: A) exactly 12 customers arrive in a given 10 minute interval (perform this calculation using an appropriate formula, showing the setup.) b) between 5 and 10 customers (inclusive) arrive in a given 5 minute interval (show how you can answer this from the table) c) after a customer arrives, find the...
3. Customers arrive at the drive-through lane of a fast food restaurant at a rate of one every 3 minutes. Use the Poisson probability distribution to answer the following (12 Marks) a. What is the expected number of customers in one hour? b. What is the probability that exactly two customers arriving at the drive-through lane in a nine-minutes interval? c. What is the probability that less than two customers arrive at the drive through lane a nine-minutes interval? d....
7.4 During lunch hour, customers arrive at a fast-food restaurant at the rate of T20 customers per hour. The restaurant has one line, with three workers taking food orders at independent service stations. Each worker takes an exponentially dis- tributed amount of time-on average 1 minute-to service a customer. Let X, denote the number of customers in the restaurant (in line and being serviced) at time t. The process (Xt)PO Is a continuous-time Markov chain. Exhibit the generator matrix
7:08 courses.yorkvilleu.ca 4 of 4 YORKVILLE 7. Customers arrive at the drive-through ane of a fast food restaurant at a rate of one every 3 minutes. Use the Poisson probability distribution to answer the following questions: (8 points) a. What is the expected number of calls in one hour? b. What is the probability that exactly two customers arriving at the drive through lane in a nine-minutes interval? c. What is the probability that less than two customers arrive at...
Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive ac cording to a Poisson process at a mean rate of 4 per minute. However, business is growing and management projects that the mean arrival rate will be 6 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 0.5 minute. Management has established the following guidelines for a satis- factory level...
Mary is a waitress in a city centre restaurant. She receives tips from customers at an average rate of λ per hour. During a particular eight a (2 marks) Let X be the number of tips Mary receives in an 8 hour period. If tips are received according to a Poisson process with rate λ tips per hour, state the distribution of X, with parameters b (5 marks) Write down the likelihood function, L(X; 5) for this problem. Remember to...
Problem 1. Consider a fast food restaurant where customers arrive and get in line according to a Poisson process with an average rate of 120 customers per hour. The restaurant has one line and the amount of time it takes the cashier to serve a customer is exponentially distributed with a mean of 2 minutes. Let X_t denote the number of customers in line at time t. 1. Give the state space of the chain (X_t)t≥0. 2. For each state...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank lobby has enough space for 10 customers. When the lobby is full, an arriving customers goes to another branch and is lost. The bank manager assigns one teller to customer service as long as the number of customers in the lobby is 3 or less. She assigns two tellers if the number is more than 3 but less than 8. Otherwise she assigns...
4 Mary is a waitress in a city centre restaurant. She receives tips from customers at an average rate of λ per hour. During a particular eight hour shift, she receives 5 tips. We wish to estimate λ. a (2 marks) Let X be the number of tips Mary receives in an 8 hour period. If tips are received according to a Poisson process with rate A tips per hour, state the distribution of X, with parameters b (5 marks)...