SOLUTION: A bus comes by every 8 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 8 minutes. A person arrives at the

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Question 1202881: A bus comes by every 8 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 8 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible.
a) The mean of this distribution is
(b) The standard deviation is
(c) The probability that the person will wait more than 6 minutes is
(d) Suppose that the person has already been waiting for 0.3 minutes. Find the probability that the person's total waiting time will be between 0.8 and 1 minutes
(e) 62% of all customers wait at least how long for the train?
minutes.
Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.

For (a) and (b)

    The uniform distribution has the following properties: 
        The mean of the distribution is μ = (a + b) / 2. 
        The standard deviation of the distribution is s = sqrt%28%28b++-++a%29%5E2%2F12%29.

        It is written in any textbook on probability.


Here a = 0;  b= 8 minutes.  So,

    μ = 8%2F2 = 4 minutes.

    s = sqrt%288%5E2%2F12%29 = sqrt%2864%2F12%29 = sqrt%2816%2F3%29 = 2.3094 minutes.



(c)  P = %288-6%29%2F8 = 2%2F8 = 1%2F4 = 0.25.



(d)  P = %281-0.8%29%2F%288-0.3%29 = 0.2%2F7.7 = 0.025974.    Round as you want.



(e)  This question is posed INCORRECTLY.

     It should ask about a bus, not about a train.   Train is irrelevant.

Solved.