Developing Expert Voices

Question #1: (March 27; Statistics)

The table shows the lengths in millimetres of 52 arrowheads.

(Didn't type out the numbers, but will create a similar question to this one.)

(a) Calculate the mean length and the standard deviation.

(b) Determine the lengths of arrowheads one standard deviation below and one standard deviation above the mean.

(c) How many arrowheads are within one standard deviation of the mean?

(d) What percent of the arrowheads are within one standard deviation of the mean length?


Question #2: (March 17; Probability)
The probability that Gallant Fox will win the first race is 2/5 and that Nashau will win the second race is 1/3.

1. What is the probability that both horses will win their respective races?

2. Wha tis the probability that both horses will lose their respective races?

3. What is the probability that at least one horse will win a race?


Time line


May 20 - Consult with the group and decide which units were going to do our projects on.

May 22 - Make sure that everyone has slowly progressed on their projects and help each other out on what their missing.

May 25 - Another group meeting, making sure everyone has got something done.

May 30 - Start putting bits an pieces of our project together.

June 3 - Complete Project

June 4 -6 - Put the finishing touches on the project

June 7 - Hand in completed assignment

Reflection on Vectors

Well Vectors is one of the shortest units ever :O. Haha, but I myself had trouble with some stuff like the Parallelogram Method, but when the pre-test came, and Mr. K showed us how it was done, I sorta got how to do it. So this unit wasn't really bad, although it was pretty confusing. So overall this unit wasn't really the best for me, but I got through it. Good luck on the test everyone, and don't forget to post your reflections!

Vectors

Soaring, flying, there's no star in heaven that we can't reach, if were trying, were breaking free. [8]

Sorry song stuck in my head just watched HSM again. Haha, so anyways, here is my blog after a 2 day rest, I already forgot what I was supposed to talk about even though I did write down notes on what I should scribe on today.

So on May 1st, which was last Friday, I was chosen by Iris (grr, don't like you =P), we had our last class of Vectors. Yipee! But which also means that there will be another test coming up which is on Tuesday. And tomorrow will be our Pre-Test, so everyone be prepared =). And also just a reminder don't forget to post your reflection for the unit Vectors.

Back to my post

So on Friday Mr. K finally finished the unit of Vectors, he also showed us another method aside from the Triangle Method. And it is called the Parallelogram Method, instead of having the vectors go from tip-to-tail. The Parallelogram Method goes from tail-to-tail.

This is how the Parallelogram Method is to be used:
















So anyways instead of 2 vectors being connected, there will be 3 vectors. Thus forming the parallelogram shape, and when you put another vector down the middle, it also forms two triangles. Also a reminder that when you are creating a diagram like this, make sure that the scale respects your diagram.

After that explanation Mr. K solved a problem with us, this problem was kinda confusing for me but it all worked out in the end, here it is:



















There really isn't much to explain any further, so all I gotta say is study hard and prepare for the Vectors test on Tuesday.

Next person I chose is Camilla for scibe! Haha.

Statistics Reflection

The Statistics Unit, was a hard but yet understandable unit. I was scared when I missed one class, which was yesterday, that I might of missed a lot of important things. But the day after that when I actually got to class in time, I understood what was given to us as a class. And I caught on quickly. The test might be a bit challenging for me as I do understand the unit, but I also get confused at times. I guess studying and looking into the problems deeper, and reviewing the slides that Mr. K puts up every night may help me. The unit was very hard for me to understand during the process of learning, but as we kept on solving problems, it came to me just like that. Hopefully I will do good on the test on Thursday!! Good luck to everyone!

Today in class we started off being broken down into groups. We then quickly checked our homework. We were then given a problem to solve, it's on the slides today March 11, slide 9.

The question was:
Suppose that, when you go home from school, you like to take as great a variety of routes as possible, and that you are equally likely to take any possible route. You will walk only east or south.

We used the Pascal's Triangle to solve how many ways we can get from School to home. The answer was 180 ways to get from School to Home.

This is how it was done:














Then we went into more depth of the question, Daniel went up and explained that there was really only a certain way to go home AND pass the post office. This is what he means. The red lines shows how many ways you can pass the post office, from school to home. The blue just shows the extra routes going from school to home, WITHOUT passing through the post office.
















So now getting back to the question which was, what is the probability of passing the post office on your way home.

The answer would be:

Number of ways from School to Home passing the post office: 72
Over the total number of ways from School to Home: 180


SO: 72 / 180 would be the probability of passing through the post office on your way home!

Reminder, always reduce fractions if possible!
Reduced fraction = 2 / 5

And the next scribe would be..

DON !

Transition Matrices (cont'd)

Well today in class, we spent most of our time reviewing the homework we had last night. And Mr. K just reviewed a little more about Transition Matrices, there was really nothing new for today.

Transition Matrices just shows you the probability of 2 or more things, if it would sell or if it will increase in days, weeks, or even years. Basically just probability of 2 or more things in the future.

I'll give you guys just another example of transtion matrices just in case some people are still not following. And hope this helps :).

Lets say you wanted to find out which air freshener would people use more in 10 years, Air Wick or Febreze.

First you would want to write the State Matrix, which means what is happening right now. So if the 20 people used Air Wick and 35 people used Febreze then the State Matrix would be as so. A for Air Wick and F for Febreze.








Here is the Transition Diagram, you can see how people change from one thing to another or if they just stay with that one product.










So, by looking at this diagram, 90% of the people that use Febreze stay with Febreze, but 10% change to Air Wick. And 70% of the people that use Air Wick stay with Air Wick, but 30% change to Febreze.

Now you have enough information to write a Transition Matrix. Here is how it will look like.










Now all you have to do is plug in the numbers, and follow the diagram above. And it will simply look like this.










And the only thing left to do is, multiply the State Matrix with the Transition Matrix. It will look like this.








You can punch this in your graphing calculator and put the State Matrix in matrix a, and the Transition Matrix in matrix b. Then just simply multiply matrix a and b, if you did it correctly you will get an answer like this.










Now you`ve got everything, you have to find out if Air Wick or Febreze was used more after 10 years. To do that, all you have to do is take your State Matrix (S) and your Transition Matrix (T) and just multiply to the power of 10. It will look like this.










So if you have punched in the matrix correctly you should have an answer like this.







If you are having trouble with transition matrices, you can also look at the nice example Alvina gave just under this post.

*Unit test coming up soon so hope you guys have been reading the posts everyday.

annnnnnnnd last but not least...

The next scribe is...
DON !