# Chapter 6 sections 1 & 2

### By: Kristen Hernandez

## Properties of 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

- a bell-shaped__Normal Curve explanation__**curve**showing a particular distribution of probability over the values of a random variable. Also called Gaussian**curve**, probability**curve**. Origin of**normal curve**Expand.

## Empirical Rule

## Empirical Rule explination

- Above the mean, the
**empirical rule**or the 68-95-99.7**rule**. tells us that there is a 99.7% chance of finding a result in a. normal distribution that is within three standard. deviations of the mean. **When do we use the empirical rule?**The Empirical Rule is often used in statistics for**forecasting**, especially when obtaining the right data is difficult or impossible to get. The rule can give you a rough estimate of what your data collection might look like if you were able to survey the entire population.- Example 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

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. These lines are determined from historical data

## Z-Scores- Calculation

- The z value or z score (also known as standard score) gives the number of standard deviations between the original measurements x and he mean of the x distribution
- The mean of the original distribution is always zero, in standard units. This is understandable because the mean is zero standard variations for itself.
- an x value is the original distribution that is above the mean u has a corresponding z value that is positive.

## What does the standard normal distribution tell us?

- The mean is 0
- the standard deviation is 1
- any normal distribution can be converted to a standard normal distribution by converting all the measurements to standard z scores.

## What does a standard score tell us?

- a standard score or z score of a measurement tells us the number of standard deviations the measurement is from the mean.
- a standard score close to zero tells us the measurement is near the mean of the distribution
- a positive standard score tells us the measurement is above the mean
- a negative standard score tells us the measurement is below the mean.