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Suppose 45% of the population has a college degree. If a random sample of size 662 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by more than 3%? Round your answer to four decimal places.

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Answer: 0.0604

Step-by-step explanation:

Given that:

Population proportion (p) = 45% = 0.45

Sample size (n) = 662

1 - p = 1-0.45 = 0.55

P - phat > 0.03

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

Using the relation :

P(Z > p - phat / sqrt((p(1-p))/n))

sqrt((p(1-p))/n) = Sqrt((0.45(0.55)/662) = 0.01933

P(Z > 0.03 / 0.0193356) = P(Z > 1.5515)

P(Z > 1.5515) = 0.0604 (Z probability calculator)