# Suppose 47% of the population has a college degree.If a random sample of size 501 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by less than 6%? Round your answer to four decimal places.

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Suppose 47% of the population has a college degree.

If a random sample of size 501 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by less than 6%? Round your answer to four decimal places.

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Step 1

It is provided that

p = 0.47, q = 1- p = 1-0.47 = 0.53 and n = 501

Consider, the sampling distribution of sample proportion follows the normal distribution, that is,

Step 2

Thus,

Step 3

Now, the required probabilit... help_outlineImage TranscriptioncloseP(-pk0.06)- P( p-0.47|< 0.06) =P(0.41< <0.53) 0.41-0.47 p- 4, 0.53- 0.47 = P 0.0223 0.0223 P(-2.6906

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