A P STATISTICS LESSON 2 – 2

1. A P STATISTICSLESSON 2 – 2 STANDARD NORMAL CALCULATIONS

2. 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.

3. 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.

4. 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

5. 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.

6. 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

7. Normal Distribution Calculations