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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 200200 mg and a standard deviation of 1010 mg. For a random sample of six bottles, the sampling distribution of the mean caffeine content has a standard error of approximately 10/6≈4.0810/\sqrt{6} \approx 4.08 mg. Consider the following events:

A: The sample mean caffeine content is greater than 205205 mg.
B: The sample mean caffeine content is less than 196196 mg.
C: The sample mean caffeine content is between 198198 mg and 202202 mg.
D: The sample mean caffeine content is between 190190 mg and 210210 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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