Final answer:
The correct answer to the question is b) Symmetrical skew, implying that the sampling distribution of the sample means is most likely symmetrical due to the Central Limit Theorem, when the sample size is large.
Step-by-step explanation:
The question addresses a concept in statistics related to the sampling distribution of sample means when drawn from a positively skewed population. If the distribution of the population is positively skewed, it means that the mode is often less than the median, which is less than the mean. When the sample size n is large, according to the Central Limit Theorem, the sampling distribution of the sample means will approximate a normal distribution. The Central Limit Theorem indicates that as the sample size becomes larger, the distribution of the sample means becomes less skewed, approaching symmetry.
Therefore, with regard to the options provided:
a) Negative skew - Incorrect, because a large sample size leads to a distribution that is less skewed.
b) Symmetrical skew - Correct, as this is what occurs when the sample size is sufficiently large, according to the Central Limit Theorem.
c) No skew - Not precisely correct, although 'symmetrical skew' is a better expression of the concept.
d) Positive skew - Incorrect, the initial positive skew of the population does not necessarily carry over to a large sample's mean distribution, which is symmetrical.
To summarize, the correct answer to the student's question is b) Symmetrical skew, meaning that the sampling distribution of the sample means is most likely to have a symmetrical distribution when the sample size is large, regardless of the initial positive skewness of the population distribution.