Prob. & Stat.
6.1 - 6.2
Normal Curve
Properties of a 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 (or variance 2)
μ - Sample Mean σ - Standard Deviation
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!
Empirical Rule
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.
Control Chart
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.
Z-Score
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.