Final answer:
The sample means of heights of adult females can be treated as a normal distribution even with a small sample size of n = 3 because the original population from which the samples are drawn is normally distributed, in accordance with the Central Limit Theorem.
Step-by-step explanation:
The question is about the distribution of sample means. According to the Central Limit Theorem, when an original population has a normal distribution, such as the heights of adult females, even a small sample size will result in sample means that are normally distributed. Specifically, in this case, where sample sizes of n = 3 are used to collect heights of adult females and calculate sample means, it is incorrect to conclude that the sample means cannot be treated as a normal distribution merely based on the small sample size. This is because the parent population of heights is normally distributed. If the population were not normally distributed, a larger sample size, typically n ≥ 30, would be necessary for the sampling distribution of the mean to be normal.
Moreover, the mean of the sample means will equal the population mean, whereas the standard error of the mean will be the population standard deviation divided by the square root of the sample size, providing a measure of variability of sample means around the population mean.