Suppose that 50% of all politicians are lawyers. If a random sample of 518 politicians is chosen, what is the probability that the proportion who are lawyers will differ from the population proportion by more than 6%
Solution
Given that,
p = 0.50
1 - p = 0.50
n = 518
_{} = p = 0.50
_{} = [p ( 1 - p ) / n] = [(0.50 * 0.50) / 518] = 0.02197
= 1 - P[-0.06 / 0.02197< ( - _{} ) / _{} < 0.06 / 0.02197]
= 1 - P(-2.73 < z < 2.73)
= 1 - P(z < 2.73) - P(z < -2.73)
= 0.0063
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