When you take a large enough random sample (n > 30), the sample mean is likely to be approximately equal to the population mean. This result is supported by the Central Limit Theorem (CLT), which states that for a sufficiently large sample size (n > 30 is a common rule of thumb), the distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution. The larger the sample, the closer the sample mean will be to the population mean, as long as the sample is representative and random.

Key points:

• For large samples (n > 30), the sample mean approaches the population mean.
• The sample mean follows a normal distribution due to the Central Limit Theorem.
• The variability of the sample mean decreases as the sample size increases.

Would you like further details on the Central Limit Theorem or its applications?

Related questions:

1. How does the Central Limit Theorem work for smaller sample sizes?
2. Why is n > 30 considered a sufficient sample size in most cases?
3. How does sample size affect the variability of the sample mean?
4. What are the assumptions behind the Central Limit Theorem?
5. How does the Central Limit Theorem apply to non-normal population distributions?

Tip:

To ensure your sample mean closely approximates the population mean, make sure the sample is random and unbiased.