SOLUTION: Please help!! A caretaker notes that on average he replaces three bulbs each month in the school in which he works. Find the probability that during a given month he needs to re

Question 983441: Please help!!
A caretaker notes that on average he replaces three bulbs each month in the school in which he works. Find the probability that during a given month he needs to replace more than four bulbs?
(1) 0.185
(2) 0.353
(3) 0.050
(4) 0.950
(5) 0.750
Please provide an explanation - I will be eternally greatful!! Thank you
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
I am assuming a Poisson function with lambda=3. The number is small, it could be infinite, and they occur sporadically, so the assumption of a Poisson is reasonable.
The multiple choice makes this easier:
I can do the probability of 0,1,2,3 and subtract it from 1. Everything else would be 4 or greater.
BUT, let me do just 4 and 5
exp(-3)3^x/x!
For x=4, that works out to 0.168
for x=5, that is e^-5(3^5/5!=0.014
x=6 will be still smaller, etc., because the further from the average, the smaller the value.
So, without computing the exact probability, I have found 0.182 is very close to the real probability and a little under. Therefore, 0.185 is the answer. A calculator would make this easier if one were so inclined.
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