Random samples of 49 are drawn from a population with mean 80 and standard deviation 21. By the central limit theorem, how is the sample mean distributed?

About normal, with mean 80 and standard error 3Correct answerYour answerAbout normal, with mean 80 and standard deviation 21Correct answerYour answerAbout normal, with mean

\frac{80}{7}

and standard error 3Correct answerYour answerExactly the same as the populationCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

For a large sample, $\bar{x}$ is roughly normal with the population's mean, 80.
Its spread is the standard error $\frac{21}{\sqrt{49}} = 3$ .

Worth noting

Sample means vary much less than single values: 3, not 21.

Concept: The central limit theorem
Typical timeTypical: 90 s
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The rule this testsParameters, statistics and the central limit theorem

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Random samples of 49 are drawn from a population with mean 80 and standard deviation 21. By the central limit theorem, how is the sample mean distributed?

Explanation