Final answer:
The distribution of sample means will be normal since the original population is normally distributed and the sample size of 16, while not exceedingly large, is moderate enough to assume normality of the sample means as per the Central Limit Theorem.
Step-by-step explanation:
When examining whether we can say anything about the distribution of sample means when random samples of size n = 16 are selected from a population with a mean (m) of 72 and a standard deviation (s) of 8, the Central Limit Theorem (CLT) is the key concept to consider. The CLT states that when the sample size is sufficiently large (usually n ≥ 30 is considered adequate), the distribution of sample means will approximate a normal distribution, regardless of the original population's distribution. However, in the case where the sample size is smaller, such as n = 16, if the population distribution is already normally distributed, then the distribution of sample means will also be normal.
Given the population mean (m) as 72 and standard deviation (s) as 8, with n = 16, the distribution of sample means will still be normal based on the provided information. This follows since the population distribution itself is normal, and the sample size, though not exceeding 30, is not extremely small either. As such, the sampling distribution of the mean will be characterized by a mean equal to the population mean, and a standard error (the standard deviation of the sample means), which is the population standard deviation divided by the square root of n, s/√n.
Therefore, the correct answer to the question is A) Yes, the distribution of sample means will be normal. This is because with a normal population distribution and a moderately sized sample (n = 16), the distribution of sample means is expected to be normal due to the CLT.