23. The Central Limit Theorem states that: (a) if n is large then the distribution of the sample can be approximated closely by a normal cur

Question

23. The Central Limit Theorem states that: (a) if n is large then the distribution of the sample can be approximated closely by a normal curve (b) if n is large, and if the population is normal, then the variance of the sample mean must be small. (c) if n is large, then the sampling distribution of the sample mean can be approximated closely by a normal curve (d) if n is large, and if the population is normal, then the sampling distribution of the sample mean can be approximated closely by a normal curve (e) if n is large, then the variance of the sample must be small.

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Piper 2 weeks 2021-09-12T06:15:20+00:00 1 Answer 0

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    2021-09-12T06:17:01+00:00

    Answer:

    (c) if n is large, then the sampling distribution of the sample mean can be approximated closely by a normal curve.

    Step-by-step explanation:

    The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample mean, with a large sample size, can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

    This is valid no matter the shape of the population.

    So the correct answer is:

    (c) if n is large, then the sampling distribution of the sample mean can be approximated closely by a normal curve.

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