# Central limit theorem/Sampling distribution of a sample mean

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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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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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From the condition, the mean is , the standard deviation ...

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