A P STATISTICSLESSON 2 – 2

STANDARD NORMAL CALCULATIONS

ESSENTIAL QUESTION: How is the Standard Normal Curve used to find

information about data?

Objectives: To find Z scores of data from normal

distributions. To use the standard normal curve to help answer

real world problems.

Standard Normal Distributions

All normal distributions are the same if we measure in units of size σ about a mean μ as center. Changing to these units is called standardizing the data.

Standardizing and Z - scores

If x is an observation from a distribution that has mean μ and standard deviation σ, the standardized value of x is

Z = x – μ

A standardized value is often called a z – score.

σ

Z - Scores

Tells us how many standard deviations the original observation falls away from the mean, and which direction. Observations larger than the mean are positive when standardized, and observations smaller than the mean are negative.

If the variable we standardize has a normal distribution, standardizing does more than give a common scale. It makes all normal distributions into a single distribution, and this distribution is still normal.

Standard Normal Distribution

The standard normal distribution is the normal distribution N( 0, 1 ) with mean 0 and standard deviation 1

If a variable x has any normal distribution N( μ, σ ) with mean μ and standard deviation σ, then the standard variable has the standard normal distribution.

Z = x - μ

σ

Normal Distribution Calculations