Standardized Scores and Normal Distribution

Coin Flipping Example:
- Consider an experiment where a coin is flipped 3 times.
- One specific outcome in the sample space is getting zero heads, which represents the explicit outcome sequence of tail, tail, tail.
Normal Distribution Parameters:
- Data values and outcomes can be distributed normally following a standard bell curve.
- The curve is mathematically defined by two primary population parameters:
- Population Mean ( $\mu$ ): Represents the population average or the central value of the distribution.
- Standard Deviation ( $\sigma$ ): Represents the standard deviation, measuring the variability or spread of the data around the mean.
- Given both $\sigma$ and $\mu$ , the exact normal curve can be drawn, enabling the calculation of relative areas under the curve corresponding to probabilities or proportions.

Need for Standardization:
- When working with old-school statistical charts and tables, raw measurements or scores cannot be directly evaluated for standard probabilities.
- The raw score must be converted into a standardized score.
Function of Standardized Scores:
- Conversion to a standardized score rescales raw data relative to the population mean ( $\mu$ ) in units of standard deviation ( $\sigma$ ).
- Standardizing allows the use of standard normal reference tables to determine precise areas under the normal curve regardless of the original raw score scale.