Question

Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever​ dogs, each of size nequals​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. Choose the correct answer below. A. ​Yes; the sample size must be over 30 for the sample means to be normally distributed. B. ​No; the original population is normally​ distributed, so the sample means will be normally distributed for any sample size. C. ​No; the samples are collected​ randomly, so the sample means will be normally distributed for any sample size. D. ​No; as long as more than 30 samples are​ collected, the sample means will be normally distributed.

Answer 1

Answer:

B.

Step-by-step explanation:

If the population, in this case, weights of golden retriever dogs, follows a normal distribution, then the sample will too, even if the sample size is lower than 30. You only have to worry about the sample size being too small when a problem doesn't explicitly say the distribution from which the samples are drawn is normally distributed.

Answer 2

According to the central limit theorem, the correct statement is:

B. ​No; the original population is normally​ distributed, so the sample means will be normally distributed for any sample size.

• The Central Limit Theorem establishes that a normal variable X, with mean $\mu$ and standard deviation $\sigma$, has sampling distribution of the sample means with size n that can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.
• The Central Limit Theorem is also valid for skewed variables, if the sample size is greater than 30.
• In this problem, the underlying distribution is normal, thus, the sampling distribution of sample means is also normal, which means that option B is correct.

A similar problem is given at https://brainly.com/question/10554762