Question

The number of people arriving at an ATM can be described by a Poisson Distribution. It is known that the mean number of arrivals in thirty minutes is 11.0.  Determine the probability that ten people or less arrive in 30 minutes. Enter your answer as a decimal rounded to three places.

Answer 1

lambda for 30 minutes is 11,

As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

P(X <= 10) = 0.460

We need to calculate P(X <= 10).
P(X <= 10) = (11^0 * e^-11/0!) + (11^1 * e^-11/1!) + (11^2 * e^-11/2!) + (11^3 * e^-11/3!) + (11^4 * e^-11/4!) + (11^5 * e^-11/5!) + (11^6 * e^-11/6!) + (11^7 * e^-11/7!) + (11^8 * e^-11/8!) + (11^9 * e^-11/9!) + (11^10 * e^-11/10!)
P(X <= 10) = 0 + 0 + 0.001 + 0.004 + 0.01 + 0.022 + 0.041 + 0.065 + 0.089 + 0.109 + 0.119
P(X <= 10) = 0.460