# Prob. & Stat.

## Properties of a Normal Curve

1. The normal curve is symmetrical about the mean μ;

2. The mean is at the middle and divides the area into halves;

3. The total area under the curve is equal to 1;

4. It is completely determined by its mean and standard deviation σ (or variance 2)

## How to find μ & σ

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.

## What is a Control Chart?

The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit and a lower line for the lower control limit.

## What exactly is a 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.

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