In 2004 the federal Department of Education reported that, nationally, the propo

Question

In 2004 the federal Department of Education reported that, nationally, the proportion of college freshmen that returned to the same school for their sophomore year was 0.74. Suppose we select a random sample of 490 freshmen from across the nation.
Question 1. What is the expected value of the sampling distribution model for the proportion of 490 freshmen that will return to the same school for their sophomore year?

Question 2. What is the standard deviation of the sampling distribution model for the proportion of 490 freshmen that will return to the same school for their sophomore year?
(Round to 3 decimal places)
Question 3. What is the probability that the proportion of these 490 freshmen that return to the same school for their sophomore year is less than 0.74?
(Round to 4 decimal places)

Explanation / Answer

Given n=490, p=0.74

(1) expected value = n*p =490*0.74 = 362.6

(2) standard deviation =n*p*(1-p)=sqrt(490*0.74*(1-0.74)) = 9.709

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