SOLUTION: Jim is a real estate agent who sells large commercial buildings. Because his commission is so large on a single sale, he does not need to sell many buildings to make a good living.

Question 1193175: Jim is a real estate agent who sells large commercial buildings. Because his commission is so large on a single sale, he does not need to sell many buildings to make a good living. History shows that Jim has a record of selling an average of 7.1 large commercial buildings every 267 days.
In a 70-day period, what is the probability that Jim will make no sales? one sale? two or more sales? (Use two decimal places for 𝜆. Round your answers to four decimal places.)
P(0)=
P(1)=
P(r ≥ 2)=
In a 93-day period, what is the probability that Jim will make no sales? two sales? three or more sales? (Use two decimal places for 𝜆. Round your answers to four decimal places.)
P(0)
P(2)
P(r ≥ 3)

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Poisson distribution events are proportional to time
so 7.1/267=lambda/70, so lambda is 70*7.1/267=1.86 buildings in 7.1 days
p(0)=e^(-1.86)=0.1557
p(1)=e^(-1.86)*1.86^1/1!=0.2896
P(>=2) is 1-0.2896-0.1557=0.5547
-
93 days
lambda is 2.47
p(0)=e^(-2.47)=0.0846
p(2)=e*(-2.47)*2.47^2/2!=0.5160
p(1)=0.0846*2.47=0.2089
p(>=3)= 1- the sum above=0.1905
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