SOLUTION: The average number of homes sold by the GBRAR is four (4) homes per day. What is the probability that exactly six (6) homes will be sold tomorrow?

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Question 1176927: The average number of homes sold by the GBRAR is four (4) homes per day. What is the probability that exactly six (6) homes will be sold tomorrow?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
I have to assume a Poisson distribution with parameter 4 to solve this.
that would be P(6)=e^(-4)*4^6/6!=0.1042

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
The average number of homes sold by the GBRAR is four (4) homes per day.
What is the probability that exactly six (6) homes will be sold tomorrow?
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            The problem does not state that the only Poisson distribution can be used.

            Therefore,  totally different  (but still reasonable approach)  can be developed and applied. 


Let's consider a random discrete variable X of the number of sold homes with integer values 
from 0 to 8 inclusive, uniformly distributed.


Such random variable satisfies the given restriction, having 4 homes per day as the average.


Then we have the discretely distributed random variable having 9 possible values from 0 to 8 inclusive
with the probability  1%2F9  for each discrete individual value.


Then  P(X=6) = 1%2F9 = 0.1111...         ANSWER

Solved  (differently).

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What is interesting,  this answer of  0.1111  is not too far from the value of  0.1042,
obtained by  @Boreal with the use of the  Poisson distribution.