Students arrive to class according to a Poisson process with lambda = 8 arrivals per minute. a. What is the probability that at least 2 students arrive in 1 minute? b. What is the probability that exactly 15 students arrive in 2 minutes? What is the distribution (with relevant parameter) of the interarrival times?
Added by Eva A.
Step 1
Using the Poisson distribution formula with λ = 8, we get: P(X = k) = (e^-λ * λ^k) / k! P(X = 0) = (e^-8 * 8^0) / 0! = 0.0003355 P(X = 1) = (e^-8 * 8^1) / 1! = 0.0026844 Show more…
Show all steps
Close
Your feedback will help us improve your experience
Adi S and 95 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
Events occur according to a Poisson process with rate $\lambda=2$ per hour. (a) What is the probability that no event occurs between $8 \mathrm{P} . \mathrm{M} .$ and $9 \mathrm{P.M.?}$ (b) Starting at noon, what is the expected time at which the fourth event occurs? (c) What is the probability that two or more events occur between $6 \mathrm{P.M}$. and 8 P.M.?
Narayan H.
The number of cars arriving at a given intersection follows a Poisson distribution with a mean rate of 2 per second. a. What is the probability that 8 cars arrive in three seconds? b. What is the probability that the time until the next arrival will be more than 1.5 seconds?
Hubert A.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD