Answer to Question #228581 in Statistics and Probability for Talha

Question #228581

If 60% of the voters in a large district prefer candidate A, What is probability that in a sample of 12 voters exactly 7 will prefer A.

can you explain this question please.?


1
Expert's answer
2021-08-23T16:14:01-0400

Let X=X= the number of voters in a sample of 12 voters who will prefer A: XBin(n,p).X\sim Bin(n, p).

Given n=12,p=0.6,q=1p=0.4.n=12, p=0.6, q=1-p=0.4.


P(X=7)=(127)(0.6)7(0.4)127P(X=7)=\dbinom{12}{7}(0.6)^7(0.4)^{12-7}

=792(0.6)7(0.4)5=0.2270303354880.22703=792(0.6)^7(0.4)^{5}=0.227030335488\approx0.22703


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