Uniform distribution: A bus arrives at a bus stop every 7 minutes. Waiting time....

Firter

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Mar 4, 2017
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Hi!

My math problem seems to be quite simple, but for some reason I can't figure it out completely. Problem is:

A bus arrives at a bus stop every 7 minutes. Waiting time for the bus is uniformly distributed between [0,7] (in minutes) and a person will use the bus 145 times per year. X is now asked to be the waiting time for the bus in seconds on a randomly chosen trip.

First, I'm asked to calculate the expected value E(X). This is straightforward, the formula a+b/2 gives me 0+7/2 = 3,5 which is 210 seconds.

Next, it is asked to calculate the variance, Var(X). The correct formula should be (b-a)^2/12 which gives me 245 seconds. I suppose this is correct, since it is a uniform distribution?

The real problem is the last part. What is the probability, that a person waits for the bus for approximately maximum 3 minutes and 50 seconds? Waiting times are independent. I could solve this easily using the uniform distribution, but I'm asked to use the normal approximation method for this example. Why would we even consider normal approximation in this example? This is the problem that I am unable to solve right now, and I'm asking for some tips. I have actually never heard about using normal approximation to a uniform distribution situation.
 
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