Answer to Question #264360 in Statistics and Probability for talie

Question

Suppose that a hair salon owner in a small town has three workers. Suppose that one client

requires the whole day to be attended due to the complexity of the styles offered by the salon

owner. Suppose that the demand is 3 requests for hair to be done per day.

(a) Find the probability that the workers are idle in a given day.

(b) The probability that the salon owner has at least one client in a day.

(b) The probability that the salon owner has excess clients in a given day.

Answer 1

Poisson distribution

$P(x=k)=\frac{\lambda^ke^{-\lambda}}{k!}$

mean:

$\lambda=3$ clients per day

a)

$P(x=0)=e^{-3}=0.0498$

b)

$P(x\ge1)=1-P(x=0)=1-1.0498=0.9502$

c)

$P(x>3)=1-P(x=0)-P(x=1)-P(x=2)-P(x=3)$

$P(x=1)=3e^{-3}=0.1494$

$P(x=2)=3^2e^{-3}/2=0.2241$

$P(x=3)=3^3e^{-3}/6=0.2241$

$P(x>3)=1-0.0498-0.2241-0.2241=0.5020$