Central limit theorem - Normal Distribution and Z-Scores

Central limit theorem

Lessons

Notes:
The distribution of sampling means is normally distributed
\cdot μx=μ\mu_{\overline{x}}=\mu
\cdot σx=σn\sigma_{\overline{x}}=\frac{\sigma}{\sqrt{n}}

Central Limit Theorem:
Z=xμxσx=xμσnZ=\frac{\overline{x}-\mu_{\overline{x}}}{\sigma_{\overline{x}}}=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}
Typically n30n \geq 30
  • 1.
  • 2.
    Comparing the Individual Z-Score 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%.
Teacher pug

Central limit theorem

Don't just watch, practice makes perfect.

We have over 310 practice questions in Statistics for you to master.