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A bus arrives approximately every half hour. Daniel arrives at a bus stopnot knowing what the schedule is. What is the probability that a busarrives in the next 20 minutes?

Question

Hi. How do you calculate this Poisson Distribution in the TI-83? Thanks.

A bus arrives approximately every half hour. Daniel arrives at a bus stop
not knowing what the schedule is. What is the probability that a bus
arrives in the next 20 minutes?
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A bus arrives approximately every half hour. Daniel arrives at a bus stop not knowing what the schedule is. What is the probability that a bus arrives in the next 20 minutes?

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Step 1

Let ‘Y’ be the waiting time between two busses which follows exponential distribution with mean waiting time 30 minutes and arrival rate 1/30. That is, 1 bus in 30 minutes.

The probability that a bus arrives in the next 20 minutes is equal to waiting time less than or equal to 20 minutes. It can be written as,

P( st) P(20)
Here, x represents the mean number of cars arriving in 30 minutes.
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P( st) P(20) Here, x represents the mean number of cars arriving in 30 minutes.

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Step 2

Let X be the number of busses arriving in 20 minutes.

So, the avera...

20
-=Y
30
2
3
0.6667
Thus, X follows Poisson distribution with 2 0.6667
The relationship between the exponential distribution and Poisson
distribution is as follows:
P(Y st) P(X, x)
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20 -=Y 30 2 3 0.6667 Thus, X follows Poisson distribution with 2 0.6667 The relationship between the exponential distribution and Poisson distribution is as follows: P(Y st) P(X, x)

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