# Chapter 6.1 and 6.2

### Clarissa McGarner

## Empirical Rule

Use this rule for a distribution that is symmetrical and bell-shaped(normal distribution):

68% data values lie within in 1 standard deviation on each side

95% data values lie within 2 standard deviations on each side of the mean

99.7% data values lie within 3 standard deviations on each side of the mean

## Control Chart

These charts are useful when examining data over a period of equally spaced time intervals or in some sequential order

You can find the mean and standard deviation by using past data from a period during the process was "in control" or

By using pecified "target" values for the mean and standard deviation

## zScores

z Score aka standard score gives the number of standard deviations between the original measurement x and the mean of the x distribution.

A standard score close to 0 tells us the measurement is near the mean of 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

## Raw Scores

If you know the mean and standard deviation of the original x distribution then all you have to do is reverse it to fin the the raw score x

x distribution with mean and standard deviation, the raw score corresponding to a z score is x=zo+u