Examples of Poisson Distribution
Example 1:
In a call centre, calls are received at an average rate of 10 calls per hour. What is the probability of receiving exactly 15 calls in an hour? Use the Poisson distribution formula.
Solution:
According to the given information, the average rate (λ) is 10 calls per hour. We have to determine exactly 15 calls in an hour; P (X = 15)
Now, putting the values in the formula of Poisson Distribution
Here e = 2.7183
P(X = 15) = 0.0347
Example 2:
A bakery sells an average of 5 croissants per hour. What is the probability that they sell no croissants in the next 20 minutes?
Solution:
According to the given information:
The average rate (λ) is 5 croissants per hour.
Time is 20 minutes or 1/3 of 60 minutes.
∴ λ = 5 × 1/3 = 5/3
We have to determine the probability of selling 0 croissants in the next 20 minutes; i.e., P (X = 0).
Now, putting the values in the formula of Poisson Distribution
P(X=0) = 0.1888
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