Question

Just before Quebec referendum on sovereignty, a local newspaper polls 400 voters in an attempt to...

Just before Quebec referendum on sovereignty, a local newspaper polls 400 voters in an attempt to predict whether it would succeed. Suppose that sovereignty has the support of 48% of the voters. What is the probability that the news paper’s sample will lead them to predict victory? Interpret the results in the context of this problem. Be sure to verify that the assumptions and conditions necessary for your analysis are met.

Math   Statistics-And-Probability   
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Answer #1

Answer: Just before Quebec referendum on sovereignty, a local newspaper polls 400 voters in an attempt to predict whether it would succeed. Suppose that sovereignty has the support of 48% of the voters.

Solution:

Mean = = 0.48

Standard deviation = √( p ( 1 - p) / n)

= √( 0.48 * 0.52 / 400)

= 0.02498

≈ 0.025

The probability that the news paper’s sample will lead them to predict victory:

P(P<0.5) = P((p - )/σ < (0.50 - 0.48)/0.025(

= P(Z < 0.80)

= 0.7881

Therefore, the probability that the news paper’s sample lead them to predict victory would be 0.7881.

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