SOLUTION: Referring to the information below, what is the probability that he will receive fewer than five calls? The probabilities that a doctor's answering service will receive 0, 1, 2,

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Question 1141832: Referring to the information below, what is the probability that he will receive fewer than five calls?
The probabilities that a doctor's answering service will receive 0, 1, 2, 3, 4, 5, 6, or 7 calls for him during lunch hour are, respectively, 0.001, 0.006, 0.022, 0.052, 0.091, 0.128, 0.149, and 0.551.
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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First, I checked that the given sequence P(0), P(1), P(2), P(3), P(4), P(5), P(6), P(7) of 8 terms monotonically increases 
and that the sum of all 8 (eight) given probabilities in the post is equal to 1 :


    0.001 + 0.006 + 0.022 + 0.052 + 0.091+ 0.128 + 0.149 + 0.551 = 1,


so the given data makes sense.



Second, the answer to the question is the sum of the first 5 (five) terms of the sequence


    P(the number of phone calls is less than 5) = P(0) +  P(1)  + P(2)  + P(3)  + P(4) = 

                                                = 0.001 + 0.006 + 0.022 + 0.052 + 0.091 = 0.172.      ANSWER