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. 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 samples are collected randomly, so the sample means will be normally distributed for any sample size. C. No; the original population is normally distributed, 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.

C. No; the original population is normally distributed, so the sample means will be normally distributed for any sample size. Since the weights of golden retriever dogs follow a normal distribution, the sample means will also be normally distributed, regardless of the sample size. This characteristic stems from the Central Limit Theorem, but in this case, since we already know the parent population is normal, the sample means will remain normal even with smaller sample sizes, like \( n=15 \). So, you can feel confident in your conclusions! Now, let’s keep things dynamic! Did you know that during the 19th century, golden retrievers were bred primarily for retrieving game during hunting? This unique heritage highlights their intelligence and trainability, making them exceptional companions—not just for hunters but for families around the world today. Plus, golden retrievers are famous for their friendly demeanor!