A university cafeteria line in the student center is a self-serve facility in which students select the food items they want and then form a single line to pay the cashier. Students arrive at a rate of about four per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customer, following an exponential distribution. (a) What is the probability that there are more than two students in the system? More than three students? More than four? (b) What is the probability that the system is empty? (c) How long will the average student have to wait before reaching the cashier? (d) What is the expected number of students in the queue? (e) What is the average number in the system?
Added by Jose Manuel H.
Close
Step 1
The arrival rate (λ) is given as 4 students per minute. The service rate (μ) can be calculated as 1 student every 12 seconds, which is equivalent to 5 students per minute. (a) The probability that there are more than two students in the system (Pn>2) can be Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 92 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A University cafeteria line in the student center is a self-serve facility in which students select the food items they want and then form a single line to pay the cashier. Students arrive at the cashier at a rate of about four per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customer, following an exponential distribution. What is the probability that there are more than two students in the system? More than three students? And more than four? (b) What is the probability that the system is empty? (c) How long will the average student have to wait before reaching the cashier? (d) What is the expected number of students in the queue? (e) What is the average number in the system? (f) Briefly explain the basic concept of queuing discipline. (g) In what kinds of situations is queuing analysis most appropriate?
Madhur L.
A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 25 per hour. It takes an average of 1.5 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. (a) Find the probability that the employee is idle. (b) Find the proportion of the time that the employee is busy. (c) Find the average number of people receiving and waiting to receive some information. (d) Find the average number of people waiting in line to get some information. (e) Find the average time a person seeking information spends in the system. (f) Find the expected time a person spends just waiting in line to have a question answered (time in the queue).
Clarissa B.
A small high school holds its graduation ceremony in the gym. Because of seating constraints, students are limited to a maximum of four tickets to graduation for family and friends. Suppose 30$\%$ of students want four tickets, 25$\%$ want three, 25$\%$ want two, 15$\%$ want one, and 5$\%$ want none. (a) Write a simulation for 150 graduates requesting tickets, where students' requests follow the distribution described above. In particular, keep track of the variable $T=$ the total number of tickets requested by these 150 students. (b) The gym can seat a maximum of 410 guests. Based on your simulation, estimate the probability that all students' requests can be accommodated.
Discrete Random Variables and Probability Distributions
Simulation of Discrete Random Variables
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD