Question

1. Find the appropriate distribution for this question. If there are 13 customers entering a restaurant per 2 minutes on average. Find the probability of having 20 or more customers entering the restaurant in a particular 2 minutes.

Answer 1

The appropriate distribution for this question is Poisson distribution.

$P(X=k) = \frac{λ^k \times e^{-λ}}{k!} \\ P(X≥20) = 1 -P(X<20) \\ = 1 - \sum^{19}_{k=0}P(λ,k)$

Mean λ=13

By Excel function

P(X<20) = POISSON(19,13,1)

= 0.9573

P(X≥20) = 1 -0.9573 = 0.0427