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.

Answer 1

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.