Central limit theorem  Normal Distribution and ZScores
Central limit theorem
Lessons
Notes:
The distribution of sampling means is normally distributed
$\cdot$ $\mu_{\overline{x}}=\mu$
$\cdot$ $\sigma_{\overline{x}}=\frac{\sigma}{\sqrt{n}}$
Central Limit Theorem:
$Z=\frac{\overline{x}\mu_{\overline{x}}}{\sigma_{\overline{x}}}=\frac{\overline{x}\mu}{\frac{\sigma}{\sqrt{n}}}$
Typically $n \geq 30$

1.

2.
Comparing the Individual ZScore to the Central Limit Theorem
A population of cars has an average weight of 1350kg with a standard deviation of 200 kg. Assume that these weights are normally distributed. 
4.
Increasing Sample Size
At the University of British Columbia the average grade for the course “Mathematical Proofs” is 68%. This grade has a standard deviation of 15%.