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Question
The average number of customers, who appear in a counter of a certain bank per minute is two. Find the probability that during a given minute three or more customers appear
Solution
The average number of customers
Who appear in a counter of a certain bank per minute = 2
∴ λ = 2
x follows poisson distribution with P(x) = `("e"^(-lambda)lambda^x)/(x!)`
P(three or more customers appears) = P(X ≥ 3)
= P(X = 3) + P(X = 4) + P(X = 5) + ……
= 1 – P(X < 3)
= 1 – {P(X = 0) + P(X = 1) + P(X = 2)}
= `1 - {("e"^-1(2)^0)/(0!) , ("e"^-1(2)^2)/(1!), ("e"^-2(2)^2)/(2!)}`
= `1 "e"^-2 [1 + 2 + 4/2]`
= 1 – 2-2 [1 + 2 + 2]
= 1 – 0.1353(5)
= 1 – 0.6765
= 0.3235
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