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

Answer 1

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