Question 552330: As a new residential area with 1000 domestic homes is going to be built,
the number of required parking lots is calculated in the following way:
We assume that there is no relation between the number of cars in
different homes. Furthermore, we assume that a domestic home has no
car with probability 0.2, one car with probability 0.7 and two cars with
probability 0.1. The number of parking lots should be planned in such
way that the probability that each car gets a parking lot is 0.99.
How many parking lots should be built? (the answer isn't 891)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! As a new residential area with 1000 domestic homes is going to be built,
the number of required parking lots is calculated in the following way:
We assume that there is no relation between the number of cars in
different homes. Furthermore, we assume that a domestic home has no
car with probability 0.2, one car with probability 0.7 and two cars with
probability 0.1. The number of parking lots should be planned in such
way that the probability that each car gets a parking lot is 0.99.
How many parking lots should be built? (the answer isn't 891)
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Expected # of cars per household = 0*0.2+1*0.7+2*0.1 = 0.9
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Expected # of cars in the community == 0.9*1000 = 900
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# of parking lots ??
Solve:
Let # of lots be "x".
900/x = 0.99
x = 900/0.99
x = 909.0909
Rounded down: x = 909
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Cheers,
Stan H.
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