SOLUTION: It is estimated that the average world birth rate is 15,000 births each hour. Assuming that these number of births per hour follows a Poisson distribution. Determine the probabil

Question 1113627: It is estimated that the average world birth rate is 15,000 births each hour.
Assuming that these number of births per hour follows a Poisson distribution.
Determine the probability of having
a. 10,000 births in a given hour.
b. 100 births in a given minute.
c. no birth in a given second.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The requirement for the Poisson Probability(P) formula is that we know the mean of observed occurrences
:
P(X, mean) = (e^-mean) * (mean^X) / X!
:
for this problem, we know the mean is 15,000 per hour
:
a) P(10000, 15000) = (e^-15000) * (15000^10000) / 10000! = 0
:
b) 15000/60 = 250
P(100, 250) = (e^-250) * (250^100) / 100! = 0
:
c) 15000/3600 = approximately 4.2
P(0, 4.2) = (e^-4.2) * (4.2^0) / 0! = 0.015
:

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