Question 1127395: On the average, ten passengers board the elevator of a bldg. every hour, what is the probability that at any randomly selected hour, the elevator will carry:
a. 15 passengers
b. 7-8 passengers
c. more than 20 passengers
Answer by ikleyn(52756)   (Show Source):
You can put this solution on YOUR website! .
I just saw (and solved) several similar problems in this forum.
They are not exactly and precisely mathematical, since the condition is not completed and requires some additions.
Again, they are not exactly and precisely mathematical, but mostly serve to exercise your "common sense".
They require you to reformulate the condition in a way the problem to obtain its sense.
And they require such an addition
a) "to be in style" (which means "to be consistent"), and
b) to be likelihood.
So, again, it is not "the pure Mathematics in its pure instance" - it is the common sense hypothesizing
to make right formulation and to get the problem solved ( = to get a likelihood solution ).
After this introduction, I can now move to the solution.
An appropriate hypotheses is to assume that we have random variable X = "the number of passenger in the elevator"
as uniformly distributed with the minimum value of 0 and the maximum value of 20.
Then the mean average is exactly 10, as the problem states, and we are
- "in style", and
- the condition becomes "self-closed".
Then the answer to the question a) is P(X=15) =  , and the answer to the question b) is P(X=7 or X=8) =  .
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