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Probability for population proportion

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In an online survey of 4,001 respondents, 8% were classified as productivity enhancers who are comfortable with technology and use the Internet for its practical value (data extracted from M. Himowitz, "How to Tell What Kind of Tech User You Are," Newsday, May 27, 2007, p F6). Suppose you select a sample of 400 students at your school, and the population proportion of productivity enhancers of 0.08.
a. What is the probability that in the sample, fewer than 10% of the students will be productivity enhancers?
b. What is the probability that in the sample, between 6% and 10% of the students will be productivity enhancers?
c. What is the probability that in the sample, more than 5% of the students will be productivity enhancers?
d. If a sample of 100 is taken, how does this change your answers to a through c?

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Answer is as below. I will appreciate if you can award more credits as I spent too much time on this.

p = 0.08

n = 400

(a)

P(p < 0.1)

= P ( Z < (0.1 - p)/sqrt(p*(1-p)/n) )

= P ( Z < (0.1 - 0.08)/sqrt(0.08*0.92/400) )

= P ( Z <1.47 )

= ...

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The solution gives detailed steps on calculating probability for population proportion. All the formula and calcuations are shown and explained.

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The solution gives detailed steps on calculating the probability for population proportion under different conditions.

Roper ASW conducted a survey to learn about American adults' attitudes toward money and happiness. 56% of the respondents said they balance their checkbook at least once a month.

a. Suppose a sample of 400 American adults were taken. Show the sampling distribution of the proportion of adults who balance their checkbook at least once a month .
b. What is the probability that the sample proportion will be within ± .02 of the population proportion?
c. What is the probability that the sample proportion will be within ± .04 of the population proportion?

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