In a population where 77% of voters prefer Candidate A, an organization conducts a poll of 19 voters. Find the probability that 14 of the 19 voters will prefer Candidate A.

(Report answer accurate to 4 decimal places. That is, round to 4 decimal places.)

We can define X the random variable of interest "number of voters that will prefer Candidate A", since we have a sample size given and a probability of success we can use the binomial distribution to model the random variable. And on this case we can assume the following distribution:

[tex]X \sim Binom(n=19, p=0.77)[/tex]

The probability mass function for the Binomial distribution is given by:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

For this problem we want to find this probability:

[tex] P(X=14)[/tex]

And usign the probability mass function defined before we got:

[tex]P(X=14)=(19C14)(0.77)^{14} (1-0.77)^{19-14}=0.1928[/tex]

Then the probability that 14 of the 19 voters will prefer Candidate A is approximately 0.1928 or 19.28%

In a population where 77% of voters prefer Candidate A, an organization conducts a poll of 19 voters. Find the probability that 14 of the 19 voters will prefer Candidate A. (Report answer accurate to 4 decimal places. That is, round to 4 decimal places.)

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In a population where 77% of voters prefer Candidate A, an organization conducts a poll of 19 voters. Find the probability that 14 of the 19 voters will prefer Candidate A.

(Report answer accurate to 4 decimal places. That is, round to 4 decimal places.)