SOLUTION: A researcher looked at the occurrence of retinal capillary hemangioma (RCH) in patients with von Hippel - Lindau (VHL) disease. RCH is a benign vascular tumor of the retina. Usin

Question 1134221: A researcher looked at the occurrence of retinal capillary hemangioma (RCH) in patients with von Hippel - Lindau (VHL) disease. RCH is a benign vascular tumor of the retina. Using a retrospective consecutive case series review, the researchers found that the number of RCH tumor incidents followed a Poisson distribution with λ = 3 tumors per eye for patients with VHL. Using this model, find the probability that in a randomly selected patient with VHL:
a. There are exactly four occurrences of tumors per eye.
b. There are more than four occurrences of tumors per eye.
c. There are fewer than four occurrences of tumors per eye.
d. There are between four and six occurrences of tumors per eye, inclusive.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
a. P(4)=e^(-3)*3^4/4!=0.1680, Poisson formula
P(3)=e^(-3)*3^3/3!=0.2204
P(2)=0.2204
P(1)=e^-3*3=0.1494
P(0)=0.0498
d. So fewer than four has probability 0.64
c. More than four is 1-P(fewer than four, and includes four)=0.1920
P(5)=0.1008
P(6)=0.0504
So d is the sum of 0.1680+0.1008+0.0504=0.3192
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