Year 12 Statistics‎ > ‎Simulations‎ > ‎Experiments‎ > ‎

Probability

Normal distribution

 
 




Lessons calendar
Learning Objectives  Material
 PROBABILITY  

Introduction to probability: equally likely outcomes

MONTY HALL PROBLEM



MONTY HALL INTERACTIVE

 

Probability trees: sample with replacement

 

TREES WITH REPLACEMENT


 

Probability trees: sample without replacement

TREES WITHOUT REPLACEMENT


 

Venn diagrams

 

VENN DIAGRAMS INTRO

VENN DIAGRAMS APPLICATIONS

 

 

Two-way tables: interpreting and completing
(or CONTINGENCY TABLES)

 

TWO-WAY INTRO



 Probability from a two-way table

 

 

PROB FROM CONTINGENCY TABLE

 
Risk and relative risk

 

 


 Expected value

EXPECTED VALUE TABLE


INSURANCE POLICY




 Continuous probability

FROM DISCRETE TO CONTINUOUS

CONTINUOUS PORBABILITY DISTRIBUTION


 

Introduction: normal distribution

 

FROM DOT TO CURVE


WHY NORMAL CURVE?


NORMALISED CURVE INTRO

 

Probability from areas

 

USING GRAPHICS CALCULATOR

USING THE GRAPH


 

Probability from tables

PROBABILITY FROM TABLES

 

Standard normal distribution

 

 AN INTRO TO 

NORMAL DISTRIBUTION


WHY STANDARD NORMAL?


 

Probabilty from Standard table

 

 

 

Applications of Normal distribution

 

CALCULATING STANDARD DEVIATION FROM AREA

68-95-99 RULE


 

Expected value for a variable normally distributed

 

 

 

Inverse normal problems & applications **

 

 
EXAMPLE 1






Probability AS91267  
Mathematics and Statistics 2.12 
Apply probability methods in solving problems 
Level  2  Credits  4  Assessment  External 
This achievement standard involves applying probability methods in solving problems. 

Achievement Criteria 
Achievement  
• Apply probability methods in solving problems. 
Achievement with Merit
• Apply probability methods, using relational thinking, in solving problems. 
Achievement with Excellence 
• Apply probability methods, using extended abstract thinking, in solving problems. 


Learning objectives 
  • evaluate statistically based reports interpreting risk and relative risk 
  • investigate situations that involve elements of chance − comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions − calculating probabilities, using such tools such as two-way tables, tree diagrams 

  • Apply probability methods in solving problems involves: 
  1. • selecting and using methods  
  2. • demonstrating knowledge of probability concepts and terms 
  3. • communicating using appropriate representations.
 
  • Relational thinking involves one or more of: 
    1. • selecting and carrying out a logical sequence of steps 
    2. • connecting different concepts or representations 
    3. • demonstrating understanding of concepts; 
    4. and also relating findings to a context or communicating thinking using appropriate 
    5. statements. 
  • Extended abstract thinking involves one or more of: 
    1. • devising a strategy to investigate or solve a problem 
    2. • identifying relevant concepts in context 
    3. • developing a chain of logical reasoning 
    4. • making a statistical generalisation; 
    5. and also where appropriate, using contextual knowledge to reflect on the answer. 

  •  Methods include a selection from those related to: 
    1. • risk and relative risk 
    2. • the normal distribution 
    3. • experimental distributions 
    4. • relative frequencies 
    5. • two-way tables 
    6. • probability trees. 

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