(14.02) When an opinion poll calls landline telephone numbers at random, approxi
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Question
(14.02) When an opinion poll calls landline telephone numbers at random, approximately 30% of the numbers are working residential phone numbers. The remainder are either non-residential, non-working, or computer/fax numbers. You watch the random dialing machine make calls. X is the number of calls until the first working residential number is reached. Does X have a binomial distribution? Give your reasons.
No, the calls are not independent. (its not this one)
No, the calls are independent, but each one has more than two possibilities.
No, the calls are independent, each one has two possibilities, but the probability of reaching a live person is not the same for each call.
No, the calls are independent, but there is no fixed number of observations.
Yes, the calls are independent, each one has two possibilities and the probability of reaching a live person is the same for each call.
Explanation / Answer
We are given that approximately 30% of the numbers are working residential phone numbers. The remaining 70% consists of either non-residential, non-working, or computer/fax numbers.
We know that in Binomial distribution, there is a fixed number of observations.
But in this case there is no fixed number of observations.
Hence option D is correct.
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