Questions: Select the appropriate word or phrase to complete the sentence. (Choose one) states that the sampling distribution of x̄ is approximately normal when the sample is large.

Select the appropriate word or phrase to complete the sentence. (Choose one) states that the sampling distribution of x̄ is approximately normal when the sample is large.

Transcript text: Select the appropriate word or phrase to complete the sentence. (Choose one) states that the sampling distribution of $\bar{x}$ is approximately normal when the sample is large.

Solution

Solution Steps

The question seems to be related to a statistical concept. The statement is likely referring to the Central Limit Theorem, which states that the sampling distribution of the sample mean $\bar{x}$ is approximately normal when the sample size is large, regardless of the shape of the population distribution.

Step 1: Understand the Question

The question is asking for a word or phrase that completes the sentence: "______ states that the sampling distribution of $\bar{x}$ is approximately normal when the sample is large."

Step 2: Identify the Concept

The concept being referred to in the sentence is a fundamental theorem in statistics that describes the behavior of sample means. This theorem is known as the Central Limit Theorem (CLT).

Step 3: Apply the Concept

The Central Limit Theorem states that the sampling distribution of the sample mean $\bar{x}$ will be approximately normally distributed, regardless of the shape of the population distribution, provided the sample size is sufficiently large.

Final Answer

The answer is: $\boxed{\text{Central Limit Theorem}}$

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