Question

Online orders for golf bags arrive to Par Inc. according to a Poisson process with rate λ=15 bags per hour. Each order contributes $90 of profit. What is the probability that within the next thirty minutes Par Inc. will realize at least $720 of profit contribution due to orders of deluxe golf bags?

Answer 1

Answer to the question)

1 bag gives profit of 90

To get profit of at least 720

number of bags needed = (720/90) = 8 bags

hence we need to find the probabilty of 8 bags minim

P(x > =8) = 1 - P(x < =7)

.

Using poission formula of probability we get:

P(X =x ) =

.

Thus P ( x= < 7) = P(X=0) + P(X=1) + P(X=2) + .. + P(X=7)

This process may manually be longer

Hence the formula of excel can help us here

The formula used in excel is as follows:

=POISSON(7,15,1)

where x = 7 ,

mean = λ = 15

last entry in the formula is 1, which implies we need the sum of probability for all values of x from 0 to 7

Hence we get P( X < =7) = 0.01800

P(X > =8) = 1-0.01800

P(X > =8) = 0.9820

Thus the probability of realizing a profit of minimum $720 is 0.9820