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.
choose the correct answer below
a. yes, the sample size must be over 30 for the sample means to be normally distributed
b. no, as long as more than 30 samples are collected, the sample means will be normally distributed
c. no, the samples are collected randomly, so the sample means will be normally distributed for any sample size
d. no, the original population is normally distributed, so the sample means will be normally distributed for any sample size

Explanation:

According to the Central Limit Theorem, if the original population is normally distributed, the sampling distribution of the sample mean will be normally distributed regardless of the sample size. Here, the weights of golden retriever dogs are normally distributed.

Answer:

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