SOLUTION: A survey is being conducted to determine public opinion concerning the construction of a refuse disposal sight in an ecologically sensitive area. Fifteen residents of the neighbour

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Question 1203269: A survey is being conducted to determine public opinion concerning the construction of a refuse disposal sight in an ecologically sensitive area. Fifteen residents of the neighbouring area are to be randomly selectedand their opinion tested. From past experience it is known that 80% of people are usually opposed to this kind of action. what is the probability that 12 of the residents will be opposed to this construction?

Answer by ikleyn(52893) About Me  (Show Source):
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A survey is being conducted to determine public opinion concerning the construction
of a refuse disposal sight in an ecologically sensitive area.
Fifteen residents of the neighbouring area are to be randomly selectedand their opinion tested.
From past experience it is known that 80% of people are usually opposed to this kind of action.
what is the probability that 12 of the residents will be opposed to this construction?
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The binomial distribution with the number of trials n= 15;
probability of "success" in each individual trial p= 0.8;
and the number of "successful" trials k= 12.


Use the standard formula for the probability


   P = C%5B15%5D%5E12%2A0.8%5E12%2A%281-0.8%29%5E%2815-12%29 = %28%2815%2A14%2A13%29%2F%281%2A2%2A3%29%29%2A0.8%5E12%2A0.2%5E3 = 0.2501   (rounded).    ANSWER

Solved.

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To see many other similar solved problems of this type,  look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
in this site.

Learn the subject from there.