Probability problem: Train arrival

[blazicekj]

Homework Statement

You take a subway every day for 23 days to get to school and back. Time of your arrival on the station is random and waiting time for a train to arrive is between 0-3 minutes. What is the probability that the sum of waiting time over 23 days is not going to exceed 80 minutes.
What conditions have you assumed to calculate this problem. Express the answer in a form of F(x) for some distribution function F.

Homework Equations

Not sure what distribution, so I can't provide them.

The Attempt at a Solution

==There's a real possibility, that I got all of this wrong, so if you think this is too long to read, feel free to skip it entirely and point me in some direction to calculate this.==

From what I gather, I can simply ignore my arrival to the station, as the waiting is still going to be ranging from 0 to 3 minutes. 23 days, twice each day, that means I have 46 random values of some continuous function. To fit into the boundary set by the 80 minute maximum, I should not exceed an average of 1.7391 waiting time for a day. Now, I seem to have a problem with the idea of distributions. I know what they are used for once I know which one to use, but how the hell do I decide which one to use? I think the train waiting time should have either uniform distribution or Normal one. And when I decide on one, do I just calculate the probability, that on interval of <0, 138> minutes, I will wait less than 80? Should I calculate the probability that the expected value of all the events will be less than 1,7391, and if so, how do I go about doing that, because I keep getting P(EX<1,7391)=1 (According to my highly non-scientific method of calculation.Allright. Sorry if I have used a different notation for something as Czech universities tend to differ in that from the rest of the world for some reason.

I know this is sort of a pre-calculus problem for you guys, but I have already passed both single and multivariable Calculus as on CTU this class is taught together with theory of information and whatnot. Which is the reason that I am asking dumb questions as this here. That class covers more material than any I have seen, all poorly written and I just don't have the time to get my head around all of it. By the way, this is an exam question from last week, so something similar may be in store for me.

Thanks.

 

[mighty2000]

Hi there,

To calculate the probability that the sum of waiting time over 23 days will not exceed 80 minutes, we first need to make some assumptions about the distribution of waiting times. As you mentioned, it is possible that the waiting times follow a uniform distribution or a normal distribution. However, we cannot make any conclusions without more information about the data.

To answer this problem, we would need to know the mean and standard deviation of the waiting times. Without this information, it is not possible to calculate the probability using a specific distribution function.

In terms of your approach, it seems like you are on the right track by considering the expected value of the waiting times. However, it is important to note that the expected value is not the same as the average. The expected value is a measure of central tendency, but it does not take into account the variability of the data. So, even if the expected value is less than 1.7391, it is still possible for the sum of waiting times to exceed 80 minutes.

To answer this problem more accurately, we would need to know the specific distribution of waiting times. Without that information, it is not possible to provide an answer in the form of F(x) for some distribution function F.

I hope this helps clarify things a bit. If you have any further questions, please don't hesitate to ask. Good luck with your exam!