What is the minimum sample size required for the Central Limit Theorem?

Question

BlackTom AI · Accepted Answer

The task asks for the minimum sample size required for the Central Limit Theorem, but this item presentation has no answer options to analyze.
First, acknowledge the missing options: without a set of choices, we cannot compare each alternative and explain why one is correct or incorrect.
Nonetheless, we can discuss the general idea behind typical rule-of-thumb guidance for the Central Limit Theorem (CLT).
The CLT states that, as sample size n grows, the sampling distribution of the sample mean tends to be approximately normal, regardless of the population distribution, provided certain conditions are met (e.g., finite variance).
A common classroom rule of thumb is n ≥ 30 for many moderately skewed or non-normal populations, which is often cited as a threshold where the normal approximation becomes reasonable for practical purposes.
Some instructors and texts prefer a more conservative threshold, such as n ≥ 40 or even n ≥ 50, especially when the underlying distribution is heavily skewed or has heavy tails.
Other contexts differentiate between population variance, skewness, and whether you are estimating a mean versus a proportion, which can shift the practical guidance.
Because the options are missing, we cannot evaluate each choice against these criteria or explain why certain thresholds are preferable in particular scenarios.
In summary, while 30 is a common baseline, many sources treat 40 as a safer minimum in more challenging distributions, and 50 in some strict analyses; the exact recommended n depends on the population shape and the precision required.
Given the absence of answer options, this explanation outlines the general considerations rather than endorsing a single labeled choice.

STAT 1450.02 SP2025 (28132) Checkpoint 15.5

What is the minimum sample size required for the Central Limit Theorem?

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