Suppose 52% of the doctors in a hospital are surgeons. If a sample of 563 doctors is selected, what is the probability that the sample proportion of surgeons will differ from the population proportion by less than 5%? Round your answer to four decimal places
Solution
Given that,
_{} = [p ( 1 - p ) / n] = [(0.52 * 0.48) / 563 ] = 0.0211
= P[(-0.05) /0.0211 < ( - _{} ) / _{} < (0.05) / 0.0211]
= P(-2.37 < z < 2.37)
= P(z < 2.37) - P(z < -2.37)
= 0.9911 - 0.0089
= 0.9822
Probability = 0.9822
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