Intro to Normal Distribution AS Maths with Liz Stats 1

Aims By the end of the lesson, you should be able to  recognise a normal distribution  understand how a normal curve works  calculate standardised scores

The normal distribution curve The normal distribution describes many naturally occurring events such as…babies’ weight, men’s height, or the number of apples grown on trees. Properties of the normal curve: It’s bell-shaped. It’s symmetrical. The mean, median, and mode all lie on the line of symmetry. The width of the curve shows how spread out the distribution is. These two have the same mean, but the black curve is more spread out. It describes situations in which very large values are rare, very small values are rare, and middling values are very common. It’s continuous.

The Spread of a Normal Distribution Curve Notation:

Example 1

You try!

Standardising Scores For normal distributions, a quicker way of determining these results is to use standardised scores (tells you how many standard deviations above or below the mean your value is). Formula in words: Formula using notation: In our previous problem… Max: Amber:

You try!

Example 2

The Standard Normal Curve The simplest normal distribution curve has a mean of 0 and a variance of 1. All other normal distributions can be related to this basic curve. Notation:

Area under the curve PAGE 24 IN YOUR FORMULA BOOKLET! The tables show the probability of getting a value less than OR less than or equal to a number. Because normal distributions are continuous, the value for less than is the same as the value for less than or equal to.

Example 3

Independent Study  Mymaths – Normal Distribution Introduction  Fully complete and mark Core 1 Past paper – JUNE 2010 DUE FRIDAY, 20 TH MARCH Optional Practise  Stats 1 textbook: Pg. 91, Ex. 4A  Stats 1 textbook: Pg. 102, Ex. 4B