SOLUTION: Good afternoon, I cannot seem to solve a statistic problem that goes like : An internet service provider claims that if any loss of service occurs before midday it will restore

Question 809602: Good afternoon,
I cannot seem to solve a statistic problem that goes like :
An internet service provider claims that if any loss of service occurs before midday it will restore the service on the same day. Past date indicate that the probability of all repairs being completed on teh same day is actually 0.7.
For the first five problems reported on a given day, what is the probability that :
a) All five will be repaired on the same day?
b) At least three will be repaired on the same day
c) fewer than two will be repaired on the same day?
I have tried the binomial option first but then realised that the outcomes are not independent, as tehy will fix teh third proble before moving on to the fourth one. Therefor I thought of poisson distribution model but if I take m =0.7, the results are very weird and unlikely. Could you please advice me on what model would be appropriate or where I am going wrong?
Thank you in advance.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Past date indicate that the probability of all repairs being completed on teh same day is actually 0.7..
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I am sure they wanted you to consider the repairs were independent.h n
Binomial with n = 5 and p(done) = 0.7 and p(not done) = 0.3
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For the first five problems reported on a given day, what is the probability that :
a) All five will be repaired on the same day?
P(x = 5) = 0.7^5 = 0.1681
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b) At least three will be repaired on the same day
P(3<= x <= 5) = 1 - binomcdf(5,0.7,2) = 0.8369
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c) fewer than two will be repaired on the same day?
P(0>= x >=1) = binomcdf(5,0.7,1) = 0.0308
Cheers,
Stan H.
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