Question 1032930: Michael is running for president. The proportion of voters who favor him is 0.3. A simple random sample of 100 voters is taken. What is the expected value, standard deviation, and shape of the sampling distribution of p? What is the probability that the number of voters who will favor Michael in the sample will be between 36 and 40? What is the probability that the number of voters who will favor Michael in the sample will be more than 26?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Michael is running for president. The proportion of voters who favor him is 0.3. A simple random sample of 100 voters is taken.
What is the expected value :: n*p = 100*0.3 = 30
standard deviation:: sqrt(n*p*q) = sqrt(30*0.7) = 4.58
and shape of the sampling distribution of p?:: binomial distribution
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What is the probability that the number of voters who will favor Michael in the sample will be between 36 and 40?
P(36<= x <= 40) = binomcdf(100,0.3,40)-binomcdf(100,0.3,35) = 0.1036
What is the probability that the number of voters who will favor Michael in the sample will be more than 26?::
P(27<= x <= 40) = 1 - P(0<= x <= 26) = 1 - binomcdf(100,0.3,26) = 0.7756
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Comment:: Modified answer to Part 3 as requested.
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Cheers,
Stan H.
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