A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.05. If 273 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.03? Round your answer to four decimal places.
Solution
_{} = [p ( 1 - p ) / n] = [(0.05 * 0.95) / 273 ] = 0.0132
P(proportion will differ from the population proportion by less than 0.03)
= P[ -0.03 / 0.0132 < ( - _{} ) / _{} < 0.03 / 0.0132]
= P(-2.27 < z < 2.27)
= P(z < 2.27) - P(z < -2.27)
= 0.9768
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