# CH.6 part 1&2 Prob and Stat

## Z-Score A Z-Score is a statistical measurement of ascore's relationship to the mean in a group ofscores. A Z-score of 0 means the score is the same as the mean. A Z-score can also be positive or negative | ## Empirical Rule The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. This rule has 3 parts: - 68% of data falls within the first standard deviation from the mean.
- 95% fall within two standard deviations.
- 99.7% fall within three standard deviations.
| ## Normal Curve - The normal curve is symmetrical about the mean μ; - The mean is at the middle and divides the area into halves; - The total area under the curve is equal to 1; - It is completely determined by its mean and standard deviation σ |

## Z-Score

A

**Z**-**Score**is a statistical measurement of a**score's**relationship to the mean in a group of**scores**. A**Z**-**score**of 0 means the**score**is the same as the mean. A**Z**-**score**can also be positive or negative## Empirical Rule

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean.

This rule has 3 parts:

- 68% of data falls within the first standard deviation from the mean.
- 95% fall within two standard deviations.
- 99.7% fall within three standard deviations.

## μ - Sample Mean σ - Standard Deviation

Calculating Standard Deviation:

- Work out the Mean (the simple average of the numbers)
- Then for each number: subtract the Mean and square the result
- Then work out the mean of those squared differences.
- Take the square root of that and we are done