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. What are the expected value, standard deviation, and shape of the sampling distribution of ?
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

a. expected value of p is p(cap) = 0.8 sample std. deviation , s = sqrt(p(cap) * (1 - p(cap) / n) = sqrt(0.8*.2/100) = 0.04 the sampling distribution has a normal distribution with mean 0.8 and std. dev. 0.04 b. P( 26

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