# STAT 1430 Lecture Notes - Lecture 18: Standard Deviation, Random Variable, Percentile

March 7, 2019

STAT1430.01—Lecture 18—Normal Distribution

-The Normal Distribution

•Type of variable: Continuous

•Shape: Symmetric (bell-shaped)

•Center: mean ! (Symmetric, so ! Median = ! Mean)

•Spread: Standard-Deviation !

-Example: Scores, times, weights, heights

-Picture

•!

-68-95-99.7 Rule: rough idea of normal probabilities (Also called the Empirical Rule)

•If the values have a normal distribution:

1) =68% lie within 1 standard deviation of the mean (!)

2) !95% within 2 standard deviation of the mean

3) !99.7% within 3 standard deviation of the mean

-Finding precise probabilities for a normal

•Standard normal (Z) distribution

-Mean !=0

-standard deviation is 1

-Values called z-scores !

μx

˜μ

μ

σx

μx

≈

≈

μz

z=x−μx

σx

1