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Question
The distribution of the number of road accidents per day in a city is poisson with mean 4. Find the number of days out of 100 days when there will be no accident
Solution
In a possion distribution
Mean λ = 4
n = 100
x follows possion distribution with
P(x) = `("e"^(-lambda) lamda^x)/(x!)`
= `("e"^-4 (4)^x)/(x!)`
P(no accident) = P(x = 0)
= `("e"^-4(4)^0)/(0!)`
= `"e"^-4`
= 0.0183
Out of 100 days there will be no accident
= n × P(X = 0)
= 100 × 0.0183
= 1.83
= 2 days .......(approximately)
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