SOLUTION: The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 52.6 %. (a). For samples of 510 voters, determine the mean and standard d

Question 965988: The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 52.6 %.
(a). For samples of 510 voters, determine the mean and standard deviation associated with the distribution of sample proportions:
The mean is
The standard deviation is
(b). Determine the probability that in a random sample of 510 voters, less than 49.7 % say they will vote for the incumbent?
The probability equals
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) P = 0.526 and Q = 1 - 0.526 = 0.474, then
mean = 0.526 and std dev = square root ( (PQ) / n ) where n is same size
std dev = square root ( (0.526*0.474) / 510 ) = 0.022110418
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mean = 0.526
std dev = 0.022110418
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b) calculate the z-score value
z-score = (X - mean) / std dev = (0.497 - 0.526) / 0.022110418 = −1.311598898 approx -1.31
consult table of z-values for the probability associated with our z-score
Probability ( X < 0.497 ) = 0.0951

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