Final answer:
The Central Limit Theorem (CLT) states that the distribution of sample means will follow a normal distribution when samples of a sufficiently large size are drawn, despite the original population distribution. Option B is the correct answer.
Step-by-step explanation:
The Central Limit Theorem (CLT) is a fundamental principle in statistics, revealing how data tends to behave when analyzed in large quantities. Specifically, the CLT addresses the distribution of sample means. According to the CLT, regardless of the population's original distribution, if we draw many samples of a sufficiently large size (n), the distribution of sample means will be approximately normal. This remains true even if the original population distribution is skewed, uniform, or has any other form.
When considering the sample mean, we are referring to the average of a set of data points drawn from a larger population. As the sample size increases, the sample means tend to form a bell-shaped normal distribution, centered around the true population mean. The standard deviation or 'spread' of the sample means will be the population standard deviation divided by the square root of the sample size, which is a measure known as the standard error.
The CLT applies to sufficiently large sample sizes, often numbering 30 or above, which is a common rule of thumb in statistics. However, with larger sample sizes, the sampling distribution's approximation to normality improves even further. For practical applications, the CLT allows statisticians to make inferences about a population based on sample data using the normal distribution.
In summary, the correct option that describes what the CLT indicates about the distribution of sample means is:
B) Follow a normal distribution