Central Limit Theorum

Question

Assume the population mean is µ=12 and standard deviation 2. By Central Limit Theorem the random sample of 121 measurements from this population would have what kind of distribution?

Answer 1

CLT says that if you sample from a population with a finite mean μ and finite standard deviation σ, then the distribution of the sample mean approaches the Normal distribution, with mean μ and standard deviation σ/√n.

 

More precisely, it says that z = (x_bar - μ) / (σ/√n) → N(0,1) as n → ∞.

 

In our case, the sample mean of will be approximately Normal with:

 

Mean: 12

Std. Dev.: 2/11