AS90289+Probability

=AS90289 Probability 2 Credits Internal 1st September 2011=

Note From the Moderators report: 90289 For Achieved the description of the simulation needs to clearly identify what a trial consists of. If limitations are discussed at Excellence level then it would be usual to require more than one such comment. Any response needs to include discussion relating to how the identified limitation would impact on the simulation process completed by the student.

http://www.studyit.org.nz/subjects/maths/math2/6/

Mathematics 2.6 Simulate probability situations, and apply the normal distribution Subject content •Probability •Normal distribution Applet Normal Distribution •Simulation

Achievement
There are two aspects to achieve:
 * You design and use a [|simulation]method to explore a situation involving probabilities. Simulations could include the use of dice and random number generators.
 * You use the [|normal distribution]model to find probabilities in straightforward problems.
 * This will require the use of [[image:http://www.studyit.org.nz/img/maths2_prob_achieve_img1.gif]]in context. (Problems will be limited to those that require the use of only one value of z.)
 * Problems could involve finding an expected number.

=Chapter 5 of your workbook=

Interesting revision (the site has quite a few relevant links and videos if you scroll down past the year 9 project details at the top).

5th August Started on A Woolly Task: We calculated the theoretical probability using a huge probability tree and a massive calculation. We compared the theoretical probability with repeated simulations of 30 and 1500 trials using a spreadsheet (below). A Woolly Task, @http://www.tki.org.nz/r/ncea/maths2_6Ev4_5nov04.doc

To describe a simulation use words and show these steps: =TT RR CC Tool Trial Repeat Record Calculate Check TT RR CC= TOOL: Explain what tool you are going to use. (Random numbers on your calculator 6RAN#+1 to get numbers 1 to 6.) TRIAL: Define what represents a successful trial. (1 represents twins, 2,3,4,5,6, represents single lambs, repeat for 4 seaons, add up the total number of lambs for that trial.) REPEAT 30 TIMES RECORD OUTCOME: Give a table of the outcomes of several trials. (30 trials - each has 4 seasons) CALCULATE: Show how to calculate required probabilities. (Add up the number of lambs in each trial and divide by 30 trials) CHECK TT-RR-CC

9th and 10th of August

11th August Guess What

15th August Fair Cop (First we completed Guess What - see above)

16th August Fair Cop - simulation

17th August We have now covered the simulations and probability questions that are required to pass. Before moving on to merit questions please ensure you have completed these four simulations, can describe the simulation and make the required calculation from your simulation results. Ensure you can answer the normal distribution questions also.



Practise Tasks with answers here: Maths/2/6 - B4 Fair Cop, @http://www.tki.org.nz/r/ncea/maths2_6Bv4_5nov04.doc or @http://www.tki.org.nz/r/ncea/maths2_6Bv4_5nov04.pdf Maths/2/6 - C4 Guess What? @http://www.tki.org.nz/r/ncea/maths2_6Cv4_5nov04.doc or @http://www.tki.org.nz/r/ncea/maths2_6Cv4_5nov04.pdf Maths/2/6 - D4 Cereal Temptations @http://www.tki.org.nz/r/ncea/maths2_6Dv4_5nov04.doc or @http://www.tki.org.nz/r/ncea/maths2_6Dv4_5nov04.pdf Maths/2/6 - E4 A Woolly Task, @http://www.tki.org.nz/r/ncea/maths2_6Ev4_5nov04.doc or @http://www.tki.org.nz/r/ncea/maths2_6Ev4_5nov04.pdf