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Probability for population proportion

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?

Solution Preview

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 )

= ...

Solution Summary

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

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