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.

(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 and standard deviation , the sampling distribution of the sample mean, with a large sample size, can be approximated to a normal distribution with mean and standard deviation .

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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