The Normal Distribution

Introduction

What is a distribution?

Why are they important?

30% of the area is in the female bar.

Proportion: 0.3 are female

Probability: .3 that officer is female

21% of the area is in the traffic bar.

Proportion: 0.21 are in traffic

Probability: .21 that an officer is in the traffic division

Can add probabilities: .42 probability that an officer is either in traffic or white collar crime

= 100.83 s = 12.62

Histogram of IQ scores

Can add areas

Histogram of IQ scores with Normal Distribution

Normal distribution is a theoretical polygon

Based on population mean and standard deviation

Whole family of distribution

Can use to model reality

Properties of the normal distribution

Peak of the curve is the mean

Symmetrical

Asymptotic

Continuous

IQ = 100 = 15

Thus 68% of IQ scores will occur between 85 and 115

Standard normal distribution

Temperature:o oF C

95

32

Distance: inchesmm

254.

Cost of a Big Mac (hypothetical)

France Japan Italy UK USA

Currency Franc Yen Lire Pound $US

Price 15.00 390.00 5500.00 1.90 1.60

Exchange Rate 3.61 61.24 1067.00 0.35 0.51

$A 4.16 6.37 5.15 5.43 3.14

Standard (Z) Scores

Formula:

zX

zX Xs

When all scores in a distibution transformed to Z scores:

= 0

s = 1

Distribution stays same