Candidate A is running for president of the student government at a large univer

Question

Candidate A is running for president of the student government at a large university. The proportion of voters who favor the candidate is 0.8. A simple random sample of 100 voters is taken.

a. Show (sketch) the sampling distribution of the p (the sample proportion) of voters who favor candidate A.

b. What is the probability that the number of voters in the sample who WILL NOT FAVOR candidate A will be between 26 and 30?

c. What is the probability that the number of voters in the sample who WILL NOT FAVOR candidate A will be more than 16?

Explanation / Answer

mean = 0.2 * 100 = 20

SD = srqt ( 0.2 * 0.8 * 100 ) = 4

b)

P( 26 - 20 / 4 < z < 30 - 20 / 4 )

P( 1.5 < z < 2.5 ) = .0668 - .0062 = 0.0606

c)

P( z > 16 - 20 / 4 )

P( z> -1 ) = 1 - 0.1587 = 0.8413

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