- #1
Gauss M.D.
- 153
- 1
Homework Statement
During a two hour window, people are given the option of calling number X, donating $9.90, or number Y, donating $0.50.
X is Poisson distributed with 1500 calls/minute. Y is Poisson with 3750 calls/minute.
What is the probability that more than $2,000,000 is raised?
Homework Equations
The Attempt at a Solution
X = number of calls to number X in 120 minutes = Po(120*1500) = Po(180000)
Y = number of calls to number Y in 120 minutes = Po(120*3750) = Po(450000)
Let Z = 9.9X + 0.5Y. We're looking for P(Z > 2,000,000).
Z should have an expectation of 1,782,000 + 225,000 = 2,007,000.
Now I want to approximate Z = Po(μ) with Z ≈ N(μ,σ). But I can't work out the standard deviation for Z. Using [itex]\sqrt{μ}[/itex] doesn't give me the right answer.