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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Asked Nov 12, 2019
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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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Expert Answer

Step 1

It is given that 47% of the population has a college degree. A sample of 501 is considered.

That is, p = 0.47 and n = 501.

The probability that the proportion of persons with a college degree will differ from the population proportion by less than 6% is P [-0.06 < (p-cap) – p < 0.06].

The required probability is, P [-0.06 < (p-cap) – p < 0.06].

The standard error required for further calculations is as shown below:

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рх. SE = п (0.47)x (1-0.47) 501 = 0.022

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Step 2

The required probability can be standardized by diving with S...

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-0.06 p- p 0.06 P(-0.06< p-p<0.06)= P| SE SE SE -0.06 = P 0.022 0.06 <Z< 0.022 =P(-2.72< Z<2.72) =P(Z2.72)-P(Zs-2.72) [Using the Excel formula, 0.9967 - 0.0033NORM.S.DIST(2.72,1) =NORM.S.DIST(-2.72,1) =0.9935

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