# Prob and Stat

## Normal Curve

• Normal curve is the 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

## μ - Sample Mean σ - Standard Deviation

Calculating Standard Deviation:

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

## What is the 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.

The empirical rule can be broken down into three 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.

## Z Score

A z-score (aka, a standard score) indicates how many standard deviations an element is from the mean. A z-score can be calculated from the following formula. z = (X - μ) / σ where z is the z-score, X is the value of the element, μ is the population mean, and σ is the standard deviation.