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Central limit theorem/Sampling distribution of a sample mean

An SRS of 400 American adults is asked, "What do you think is the most serious problem facing out schools?" Suppose that in fact 30% of all adults would answer "drugs" if asked this question. The proportion X of the sample who answers "drugs" will vary in repeated sampling. In fact, we can assign probabilities to values of X using the normal density cuve with mean 0.3 and standard deviation 0.023. Using this density curve to find the probabilites of the following events:
a)At least half of the sample believes that drugs are the schools' most serious problem.
b)Less than 25% of the sample believes that drugs are the most serious problem.
c)The sample proportion is between 0.25 and 0.35.

Solution Summary

The solution discusses An SRS of 400 American adults is asked, "What do you think is the most serious problem facing out schools?" Suppose that in fact 30% of all adults would answer "drugs" if asked this question. The proportion X of the sample who answers "drugs" will vary in repeated sampling. In fact, we can assign probabilities to values of X using the normal density cuve with mean 0.3 and standard deviation 0.023. Using this density curve to find the probabilites of the following events:
a)At least half of the sample believes that drugs are the schools' most serious problem.
b)Less than 25% of the sample believes that drugs are the most serious problem.
c)The sample proportion is between 0.25 and 0.35.

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