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A poll is given, showing 70% are in favor of a new building project. If 9...

A poll is given, showing 70% are in favor of a new building project.

If 9 people are chosen at random, what is the probability that exactly 6 of them favor the new building project?

Math   Statistics-And-Probability   
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Answer #1

A poll is given ; 70% of the subjects are in favour of a new building project.

9 people are chosen at random.

So, if X be the number of people out of these 9 who favour the new building project, then X follows binomial distribution with parameters n=9 and p=0.7.

We have to find the probability tha exactly 6 of them favour the new building project.

So, basically we have to find P(X=6).

Now, the PMF of X is

Where,

So, we have to find

So, the probability that exactly 6 out of 9 randomly selected persons favour the building project, is 0.2668.

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