## Michael is running for president. The proportion of voters who favor Michael is 0.8. A random sample of 100 voters is taken. a.

Question

Michael is running for president. The proportion of voters who favor Michael is 0.8. A random sample of 100 voters is taken.

a. What are the expected value, standard deviation, and shape of the sampling distribution of image from custom entry tool?

b. what is the probability that the number of voters in the sample who will not favor michael will be more than 16?

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3 weeks 2021-09-26T05:52:43+00:00 1 Answer 0

Michael is running for president. The proportion of voters who favor him is 0.3. A simple random sample of 100 voters is taken.

a)

What is the expected value :: n*p = 100*0.8 = 80

standard deviation:: sqrt(n*p*q) = sqrt(80*0.2) = 16

where q is proportion of voters who do not favor Michael. (q=0.2)

and shape of the sampling distribution is binomial distribution  which is  approximately a  bell shaped.

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what is the probability that the number of voters in the sample who will not favor Michael will be more than 16

P(X < 16.0) = P((x – 20) / 4.0) < (16.0 – 20) / 4.0) = P(Z < -1.00) = .1587

P(X > 16.0) = 1 – 0.1587 = 0.8413