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In this problem, it is said that 60 % of the community favored building a health center in their neighborhood.
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14 citizens are chosen at random.
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We need to find the probability that exactly 5 of them favor the building of the health center.
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So let us consider a random variable x and let this random variable x denote the number of citizens out of those 14 citizens chosen who favor the building of the health center.
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And this random variable x follows a binomial distribution.
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Now the reason for this is that all 4.
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Conditions for being a binomial distribution are satisfied.
00:36
The first condition is that the number of trials n should be fixed.
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Here we have selected 14 citizens, so n is fixed at 14.
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The second condition is that all of the trials should be independent.
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In this case, they are.
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This is because whether one citizen favors the building of the health center, it does not affect in any way or form what the other citizens think of this issue.
00:58
Now, the third condition is that there should be exactly two outcomes.
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One is a success...