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

Break Down the Problem

1. Identify the central limit theorem (CLT) and its implications for sampling distributions.
2. Determine the necessary conditions for the sampling distribution of the sample mean to be approximately normal.

Relevant Concepts

1. According to the Central Limit Theorem, the sampling distribution of the sample mean is approximately normal if the sample size is sufficiently large. A common rule of thumb is:
   • A sample size of $n \geq 30$ is considered large enough for the means to be approximately normally distributed, regardless of the population distribution.

Analysis and Detail

1. Evaluate the options provided (10, 5, 100, 2) against the rule of thumb for sample sizes:
   • Sample size 10: Not typically large enough.
   • Sample size 5: Definitely not large enough.
   • Sample size 100: More than sufficient (greater than 30).
   • Sample size 2: Far too small.

Verify and Summarize

1. Among the given options, the only sample size that meets the criteria for the sampling distribution of the sample mean to be approximately normal is 100.

Final Answer

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