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AP Statistics/Unit 5: Sampling Distributions
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Ranking Probabilities for a Sample Mean
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An energy drink has a caffeine content that is normally distributed with a mean of $$200$$ mg and a standard deviation of $$10$$ mg. A box contains six bottles; hence, the sampling distribution of the average caffeine content per box has a standard error of approximately $$10/\sqrt{6} \approx 4.08$$ mg. Rank the following events in order of increasing probability:

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

Express your answer as an ordering of the event labels (for example, “A, B, C, D”).

A

A, C, D, B

B

B, C, A, D

C

B, A, D, C

D

A, B, C, D

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