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18#Suppose that 56% of the population of U.S. voters favors a particular presidential candidate. If a random sample of 50 voters is chosen, approximate the probability that fewer than 25 favor this candidate. Use the normal approximation to the binomial with a correction for continuity.Round your answer to at least three decimal places. Do not round any intermediate steps.AGAIN Round your answer to at least three decimal places. Do not round any intermediate steps.



Answer :

We will use a correction factor of 0.5. Then:

P(X<=25.5)

The normal distribution mean:

[tex]np=50\times0.56=28[/tex]

The normal distribution standard:

[tex]\sqrt{np(1-p)}=\sqrt{28\times(1-0.56)}=3.5099[/tex]

Then:

[tex]Z=\frac{x-\mu}{\sigma}=\frac{25.5-28}{3.5099}=-0.7122[/tex]

From the normal distribution table, the probability is 0.239

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