Question

Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever​ dogs, each of size n​15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too​ small? explain.

Answer 1

The original population is normally​ distributed so that the sample means will be normally distributed for any sample size.

What is Central Limit Theorem?

The Central Limit Theorem establishes that a normal variable X, with mean $\mu$ and standard deviation $\sigma$ , has a sampling distribution of the sample means with size n that can be approximated to a normal distribution with mean and standard deviation.

$s= \dfrac{\sigma}{\sqrt{n} }$

The Central Limit Theorem is also valid for skewed variables if the sample size is greater than 30.

The underlying distribution is normal, thus, the sampling distribution of sample means is also normal.

So, The original population is normally​ distributed so that the sample means will be normally distributed for any sample size.

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