Lesson 4 Mario one of the owners of Mi Casa Front Porch Rest

Lesson 4 Mario, one of the owners of Mi Casa Front Porch Restaurant was looking to improve his planning for capacity. In order to do this, he wanted to understand the probability of people in each party coming to the restaurant. If the mean number of people per party is 3, what is the probability that the party will be 2 or 4 using the Poisson distribution? How would this influence Mario and his planning for capacity at the restaurant?

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
a)
P( X < = 2) = P(X=2) + P(X=1) + P(X=0)
= e^-3 * 3 ^ 2 / 2! + e^-3 * 2 ^ 1 / 1! + e^-3 * ^ 0 / 0!
= 0.4232

P( X < 4) = P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= e^-3 * 2 ^ 3 / 3! + e^-3 * ^ 2 / 2! + e^-3 * ^ 1 / 1! + e^-3 * ^ 0 / 0!
= 0.6472
P( X > = 4 ) = 1 - P (X < 4) = 0.3528

P( X < = 2 OR X > = 4) = 0.4232+ 0.3528 = 0.776