SOLUTION: 1.) The commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH, have a waiting time during peak rush hour periods of eight minutes ("2012 annua

Question 1186175: 1.) The commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH,
have a waiting time during peak rush hour periods of eight minutes ("2012 annual report," 2012).
a.) State the random variable.
b.) Find the height of this uniform distribution.
c.) Find the probability of waiting between four and five minutes.
d.) Find the probability of waiting between three and eight minutes.
e.) Find the probability of waiting five minutes exactly.

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52784)   (Show Source): You can put this solution on YOUR website!
.
1.) The commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH,
have a waiting time during peak rush hour periods of eight minutes ("2012 annual report," 2012).
a.) State the random variable.
b.) Find the height of this uniform distribution.
c.) Find the probability of waiting between four and five minutes.
d.) Find the probability of waiting between three and eight minutes.
e.) Find the probability of waiting five minutes exactly.
~~~~~~~~~~~~~~~~~~~

(c) P = = . You take duration of waiting time inside the base interval of 8 minutes, and relate it to the duration of the base interval. It is how the uniform distribution works. (d) P = = . The same logic works. (e) P = .

/////////////////

The note, made by @greenestamps regarding my solution is right.

My answer to question (e) is incorrect, so please IGNORE it.

Use the answer given by @greenestamps.

\\\\\\\\\\\\\\

@greenestamps, I am so sorry for my reaction - I really was wrong . . .

I incorrectly read and misinterpreted this question.

Surely, my reaction was far out of the norm, I deeply regret about it.

It was like an eclipse of my mind.

Please accept my apologies . . .

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Using the logic stated in the response from tutor @ikleyn....
c.) 5-4 1 P = ----- = - 8 8 d.) 8-5 3 P = ----- = - 8 8 e.) 5-5 0 P = ----- = - = 0 8 8

The probability of waiting ANY EXACT amount of time is zero.

The method used in tutor @ikleyn's response is exactly the way to answer these questions. The probability of waiting between A and B minutes is the difference between those two times, divided by the length of the whole interval.

So, as I showed in my response, her answers for parts c and d are correct.

But in her response for part e, she does not use that calculation. In part e, the beginning and ending times of the prescribed interval are the same, so the difference in the two times is 0, so the probability of waiting exactly 5 minutes (or any other exact amount of time) is 0.

In her response, she states (with no justification and no calculations) that the probability of waiting exactly 5 minutes is 5/8. Note that is the same probability as for part d; that means the probability of waiting between 3 and 8 minutes is the same as the probability of waiting exactly 5 minutes -- which means the probability of waiting anywhere between 3 and 5 minutes or between 5 and 8 minutes is zero.

Totally absurd...!

I here post in its entirety, with my editing, the arrogant addendum tutor @ikleyn posted on her response after seeing my response. Now she won't be able to erase it from her response; that way the whole world will be able to see what kind of a person she is.

Regarding the post by @greenestamps, I am   PERPLEXED.

My note: Yes, you certainly are....

From one side, following my post and my logic, @greenestamps correctly re-wrote parts (c) and (d) from my post.
Thank you, @greenestamps, for popularizing my solution.

I simply showed that her method for getting the answers was right; with her defensive nature, she chose to mock me for repeating what was in her response.

From the other side, in part (e) he writes p = = = 0,
saying that the probability of waiting ANY EXACT amount of time is zero.

First, notice that my post in part (e) states something very different from it:
namely, it states that   P =   in this case, and it is CORRECT.

I did not attribute to you the statement that the probability of waiting exactly 5 minutes is 0. My response instead showed that the CORRECT answer for part e is 0.

Absolutely my response states something different than yours, because your response is WRONG!

So, if @greenestamps wants to disprove me, then he is wrong TWICE:
        1) he attributes me the statement, which I did not make,

I did not attribute anything to you; I used your correct method for getting the answer to show that your answer is incorrect.

    and
        2) on the way he is wrong CONCEPTUALLY, saying that the probability of waiting any exact amount of time is zero.

Sorry, arrogant lady; that statement is correct.

Reagrding part 1), everything is clear;
regarding part 2), it is the same as to say that it is not possible in classic mechanic to measure exactly 5 minutes.

Not at all a good argument.

It's more like saying that the probability of taking the interval from 0 to 8 on a number line and asking for the probability of picking the point 5. The interval has length 8; the point has 0 width; the probability is 0.

If you, @greenestamp, will tell it to any physicist, he, probably, will not argue with you;
simply will twist a finger to the temple.

Regarding attributing me statements, which I did not make, this trick of making dispute is as old as the world,
and it is called DEMAGOGY.

Proclaiming that your wrong answer is correct is what demagogy is....

It is not the first time, when @greenestamps uses this way to argue in his discussions with me.
He just did it more than once in the past.
In the scientific and engineering communities, such tricks making dispute traditionally cause disgust.

In ANY community, your arrogance and your way of denigrating others causes disgust

\\\\\\\\\\\\\\\\

The bottom line for you, the reader, is that all my statements in my post are correct.

Not so....

Statements (c) and (d) in the @greenestamps' post, repeating my (c) and (d), are correct, too.

Yes, that's what I said in my post....

Statement (e) in the @greenestapmp's post is wrong.

No, ma'am. YOUR answer for part e is wrong.

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