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AP Statistics/Unit 5: Sampling Distributions
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Ranking Probabilities for a Sample Mean
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The caffeine content of an energy drink is normally distributed with a mean of $$200$$ mg and a standard deviation of $$10$$ mg. For a random sample of six bottles, the sampling distribution of the mean caffeine content has a standard error of approximately $$10/\sqrt{6} \approx 4.08$$ mg. Consider the following events:

A: The sample mean caffeine content is greater than $$205$$ mg.
B: The sample mean caffeine content is less than $$196$$ mg.
C: The sample mean caffeine content is between $$198$$ mg and $$202$$ mg.
D: The sample mean caffeine content is between $$190$$ mg and $$210$$ mg.

Which of the following correctly orders these events from least probable to most probable?

A

A, B, C, D

B

B, C, A, D

C

B, A, D, C

D

A, C, D, B

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