Question

Given a sample size n, how will the distribution of the sample mean behave?

Answer 1

Answer:
Provided that the sample size, n, is sufficiently large (greater than 30), the distribution of sample means selected from a population will have a normal distribution, according to the Central Limit Theorem.

Explanation:
1. As n increases, the sample mean approaches the population mean
   (The Law of Large numbers)
2. The standard error of the sample is
     σ/√n
     where σ = population standard deviation.
     As n increases, the standard error decreases, which means that the error    
     between the sample and population means decreases.