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An article stated, "Surveys tell us that more than half of America's college graduates are avid...

An article stated, "Surveys tell us that more than half of America's college graduates are avid readers of mystery novels." Let p denote the actual proportion of college graduates who are avid readers of mystery novels. Consider a sample proportion that is based on a random sample of 225 college graduates.

(a) If p = 0.5, what are the mean value and standard deviation of ? (Round your answers to four decimal places.)

mean     
standard deviation     


If p = 0.6, what are the mean value and standard deviation of ? (Round your answers to four decimal places.)

mean     
standard deviation     


Does have approximately a normal distribution in both cases? Explain.

Yes, because in both cases np > 10 and n(1 − p) > 10.No, because in both cases np < 10 or n(1 − p) < 10.    No, because when p = 0.5, np < 10.No, because when p = 0.6, np < 10.


(b) Calculate P( ≥ 0.6) for p = 0.5. (Round your answer to four decimal places.)


Calculate P( ≥ 0.6) for p = 0.6.


(c) Without doing any calculations, how do you think the probabilities in Part (b) would change if n were 400 rather than 225?

When p = 0.5, the P( ≥ 0.6) would decrease if the sample size was 400 rather than 225. When p = 0.6, the P( ≥ 0.6) would decrease if the sample size was 400 rather than 225.When p = 0.5, the P( ≥ 0.6) would decrease if the sample size was 400 rather than 225. When p = 0.6, the P( ≥ 0.6) would remain the same if the sample size was 400 rather than 225.    When p = 0.5, the P( ≥ 0.6) would remain the same if the sample size was 400 rather than 225. When p = 0.6, the P( ≥ 0.6) would decrease if the sample size was 400 rather than 225.When p = 0.5, the P( ≥ 0.6) would remain the same if the sample size was 400 rather than 225. When p = 0.6, the P( ≥ 0.6) would remain the same if the sample size was 400 rather than 225.

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