Average passanger waiting time - probability density function - normal distribution
Hello guys, so we got this additional task to solve for a post-modul at university:
- The intermediate arrival time of a bus is normal distributed
- The expected value of the intermediate arrival time during rush hour is 4 minutes
- The standard deviation of the intermediate arrival time is 50 sec (50/60min)
A passanger enters the bus stop at a random time (statistically evenly distributed).
- What will be his waiting time for the next bus. How does the distribution (probability density function) for the passangers waiting time look like?
- What is the expected average waiting time of the passanger?
- Define the standard deviation of the passangers waiting time?
- Define the probability that the passanger has to wait more than 5 Minutes during rush hour?
I now how to solve it with a fixed arrival time of 4 minutes and how to get the standard deviation for that, but not how to solve it with a normal distribution and how to bring in the standard deviation. Our professor mentioned something about forward recurrence time, but I couldn't find anything about that. Hope someone can help me out here.
Edit: An R Code would be fine too.

7
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
779
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 932 views
- $10.05
Related Questions
- Help structure linear mixed effects model random effects structure
- Questions for Statistics Project
- ANCOVA: R Squared and Partial Eta Squared
- applied probability
- Relative percentage increase / decrease
- In each of the situations, state whether the indicated model can be regarded as a Generalized Linear Model (GLM) and give reasons for your answer.
- Classification problem using one or more Simple Linear Perceptron
- Writing a conclusion about data shown in Xbar and R control charts