anonymous
  • anonymous
There are 25 students at a bus stop. It is known that on average, 3 buses arrive at the bus stop in every 20 minutes. What is the probability that the waiting time for the next bus is at least 30 minutes? State the assumptions you need to compute the above probabilities.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
I believe it has got to do with Poisson distribution but I am not sure how to start from it. :(
anonymous
  • anonymous
So the number of buses has become the interval instead? But isn't time the only unit for the interval in poisson?
anonymous
  • anonymous
Also, the question asked for the assumptions that were made in computing the probabilities. What assumptions have we made in this calculation? I don't understand what kind of assumptions have we made.

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anonymous
  • anonymous
nice prof pic lol..
anonymous
  • anonymous
Also, to have X~Pois(20/3), and find P(X>=30)=1-P(X<30), The P(X<30) is very close to 1. This would make P(X>=30)=1-1=0, which looks weird.
Zarkon
  • Zarkon
wouldn't it be Poisson\(\displaystyle\left(\frac{3}{20}\cdot 30\right)\)=Poisson(4.5)
Zarkon
  • Zarkon
Calculate P(X=0)
anonymous
  • anonymous
Why calculate the probability of X=0?
Zarkon
  • Zarkon
0 buses arriving in the first 30 mins
anonymous
  • anonymous
OHH!!! wow!! This is smart!
Zarkon
  • Zarkon
time to teach..be back later
anonymous
  • anonymous
wow! this feels counter intuitive but somewhat logical. i wouldn't have thought of it. It's like so there is zero buses during the first 30mins and so this probability is as good as there is at least a bus after this first 30mins. thanks!!
anonymous
  • anonymous
ok sure! Thanks for you help!!!

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