On weekdays from 11:30 am to 2:00 pm customers arrive at a hotdog street vendor at the rate of 24 per 30 minute interval. Assume that this process can be well modeled by the Poisson distribution. (a) What is the probability that the the vendor will have a customer within 5 minutes? (b) What is the probability that the vendor will have to wait at least 3 minutes for a customer
Added by Shaun B.
Step 1
Given that 24 customers arrive every 30 minutes, we can calculate the rate as 24/30 = 0.8 customers per minute. (a) The probability that the vendor will have a customer within 5 minutes can be calculated using the Poisson distribution formula: P(X=k) = (λ^k * Show more…
Show all steps
Close
Your feedback will help us improve your experience
Sri K and 78 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
An entrepreneur opened a small hardware store in a strip mall. During the first few weeks, business was slow, with the store averaging only one customer every 20 minutes in the morning. Assume that the random arrival of customers is Poisson distributed. a. What is the probability that at least one hour would elapse between customers? b. What is the probability that 10 to 30 minutes would elapse between customers? c. What is the probability that less than five minutes would elapse between customers?
Cheng Z.
An entrepreneur opened a small hardware store in a strip mall. During the first few weeks, business was slow, with the store averaging only one customer every 20 minutes in the morning. Assume that the random arrival of customers is Poisson distributed. (a) What is the probability that at least 1 hour would elapse between customers? (b) What is the probability that 10 to 30 minutes would elapse between customers? (c) What is the probability that less than 5 minutes would elapse between customers?
Qudsiya A.
In a waiting line situation, customer arrivals occur around the clock at a rate of six per day, and the service occurs at one every three hours. Assume the Poisson distributions. a. What is service rate (in hours)? What is the arrival rate in hours? b. What is the probability that 2 orders arrive in 6 hours? c. Find probability that at least one order arrives in 3 hours.
Christopher D.
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