The sampling distribution of sample mean for a large population is approximately normal if the sample size is ans. 2 10 100 5

Break Down the Problem

1. Identify the condition under which the sampling distribution of the sample mean approaches normality.
2. Examine the options provided to see which sample size meets this condition.

Relevant Concepts

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal if the sample size is sufficiently large. A common rule of thumb is that a sample size of $n \geq 30$ is considered large enough for the sampling distribution to be approximately normal.

Analysis and Detail

1. Sample Size Analysis:
   • 2: Too small to ensure normality.
   • 10: Still below the typical threshold for normal approximation.
   • 100: Well above the threshold, indicating a strong approximation to normality.
   • 5: Too small, similar to 2 and 10.

Verify and Summarize

The sample sizes of 2, 5, 10 do not satisfy the condition commonly set by the Central Limit Theorem. Only a sample size of 100 meets the requirement for approximating normality in the sampling distribution of the sample mean.

Final Answer

100 is the sample size that ensures the sampling distribution of the sample mean is approximately normal.