Just before a referendum on a school budget, a local newspaper polls 407 voters to predict whether the budget will pass. Suppose the budget has the support of 52% of the voters. What is the probability that the newspaper's sample will lead it to predict defeat?
Solution
Given that,
p = 52% = 0.52
1 - p = 1 - 0.52 = 0.48
n = 407
_{} = p = 0.52
_{} = p ( 1 - p ) / n
_{} = (0.52 * 0.48) / 507 = 0.0222
P( < 0.5) =
= P(( - _{} ) / _{} < (0.5 - 0.52) / 0.0222)
= P(z < -0.90 )
= 0.1841
Probability = 0.1841
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