The normal distribution Mini whiteboards – label with anything you know about the curve

Proportions for bell shaped or Normal distribution For this type of distribution, the proportions of data lying within a given number of standard deviations from the mean are approximately < -3-3 to -2-2 to -1-1 to 00 to 11 to 22 to 3>3

Normal Distribution lesson 1 Recap video lesson The standard normal distribution Using tables

Introduction-estimating heights

Notation

Mean and median

Discrete random variables and continuous random variables Discrete random variables can be tabulated using individual values Examples Continuous random variables can not be tabulated using individual values Examples

Have a go Exercise A

Activity Exercise A or Tarsia puzzle in groups of 3-4

Recap There are an infinite number of normal distributions Normal distributions have a symmetrical bell shape A Normal distributions is an example of a continuous distribution The total area under a normal distribution curve = 1 Generally for a normal distribution X ~ N(μ, δ 2 )

How many normal distributions are there?

The standard normal distribution The standard normal distribution has mean = 0 and variance = 1. It is written Z ~ N(0, 1 2 ) or more simply Z ~ N(0, 1) Φ(z) = P(Z < z) phi Eg P( Z < 1.18) = to 4 dp or Φ(1.18) =

Eg P( Z < 1.18) = P(Z< 0.95) =

Standardising a Normal Distribution X ~ N( μ, σ 2 ) can be transformed into the random variable Z ~ N( 0, 1 ) by the formula: The random variable X ~ N ( 50, 16 ). Find P(X < 53)

The random variable X ~ N(50,16). Find P(X ≤45)