Tut 3-1 part II

We decided that today was a no - blog day. (for a couple of reasons) One being that Shawn said he would blog but did not. SO now he has to do 2 days in a row. He can do Monday's lesson on RRSP's. Thanks Shawn!!!

Personal Finance - Oct. 28th

Today's class was a continuation of the subject Personal Finance! Yay! (haha)

We learnt the following: :)

TSX: Toronto Stock Exchange

TVM: Time Value Of Money

-You can access the Financial part of your graphing calculator by prressing "2nd function" then "x-1"(finance) on a regular TI-83 graphing calculator. We were then introduced to the following terms:

N= Total # of payments I%= Annual Interest rate as a percent

PV= Present Value PMT= Payment each period

FV= Future Value P/Y= # of Payments a Year

C/Y= # of Compounding periods a Year

Annual= 1 time a year

Semi-Annual= 2 times a year or every 6 months

Quarterly= 4 times a year or every 3 months

Monthly= 12 times a year or every month

Daily= 365 times a year or everyday

~Rule Of 72= Time for your interest to double.

Ex: At 8%, 72/8 = 9. meaning it will take 9 years for your money to double.

*After going over a few examples and practice questions, we were then assigned to try

Tutorial # 4.1, Page.152, # 2,6.*

*~Desiree Rantala

free cars

who wants free cars?
http://www.daveramsey.com/etc/lms/drive_free/player.cfm

Gaining confidince

The main rule for todays class on confidince intervals is the 95% confidince interval and margin of error. To find the confidince interval first you must find meu (average) and the standerd divation ( the square root of n*p*(1-p)). To find 95% interval times the standerd divation by 1.96 and add and minus it from the average. The margen of error is what you add or minus from the average to get the 95% interval. To find the percent margen of error just find the pecent with with the margen of error.

Tutorial 3.5

Today we learned how to do a Normal Approximation To A Binomial Distribution.
If npq is bigger than 10 we use Shade Norm of Invert Norm for a binomial distribution.
If npq is less than 10 we use binompdf.
n= number of trials p= probability of success q= probability of failure

STEPS:
1) find npq
2) check if npq is greater than 10
(if yes) (if no)
3) find mean 3) binompdf (n,p) store in L2
4) calc. z scores 4) fill down L1
5) shade Norm 5) answer question

SHADE NORM / INVERT NORM

Reena LeGall has signed in

Invert norm: find raw score, mean or standard deviation.
given % ------> Z-score

Opposite to Shade norm (shade norm finds the %)
Given Z - score ------> %

invert norm (0.84) = 84% -----> Z = .99
.99 is the Z score that cuts off the bottom 84%
Invert norm gives the Z score that gives % to the left of the Z score.

**** ASK % or PROBABILITY = SHADE NORM****
**** GIVES YOU % ASKING RAW SCORE = INVERT NORM****

Reena LeGall has signed out

Is This For Real?

Basically, Yes.

Standard Normal Distribution

Today in class we learned how to find "z-scores", and how normal distribution can be used in every problem for any data.
Z-scores represent how far or below the average.
To calculate a z-score, subtract the mean from the given value, x, then divide by the standard deviation.

To find a solution to a z-score problem, follow these steps:
1) Find the z-scores
2) Set the window on your calculator
3)Find the Shadenorm
4)Find the percentage

The window on your calculator for z-scores should be:
xmin:-5
xmax:5
xscl:1
ymin:-2
ymax:.5
yscl:.1
xres:1

Tut 3.3 Normal Distribution

The bell shaped curve is the graph of a normal distribution.



Every normal distribution is identified by its mean, and its standard deviation.
<--WE NEED TO KNOW!

68-95-99 rule:

• 68% of the data are within 1 standard deviation of the mean


• 95% of the data are within 2 standard deviation of the mean


• 99.7% of the data are within 3 standard deviations of the mean

The name of the part that strikes the bell is called a clapper.

tut 3-3 notes

here are today's notes. Justin will post

October 9th AND October 13th

The 40S Applied Math Class Blog for Oct.9th AND Oct 13th.

<-- This is an example of Standard Deviation.




PDF: Probability Distribution Frequency


Standard Deviation: a numerical measurement of a set of datas variability.


High standard deviation means that the set of data is spread out, where a low standard deviation means that the data is close together.





On Friday, we ewre given a worksheet that helped us explain the difference between a sigma and a sample. If you are finding the SD of a population then you would use sigma, as opposed to using a sample when estimating the "sample" of a population. We were also given 2 other worksheets, 1 which we were to hand in. The worksheet that was to be handed in was called Understanding Standard Deviation, and the other was an introduction to mean, median, & Standard Deviation.





Today, we were reminded about finishing our "Understanding Standard Deviation" worksheet, which was a excellent way to be introduced to histograms.We then got to pull out our graphing calculations for some more work involving histograms and Standard Deviation. After that, we were introduced into a VERY IMPORTANT formula. it is called the NPQ formula and it is displayed as follows: -Mean = np and SD= the square root of (np x (1-q)


p = the probability of success, q = the probability of failure, and n = the # of trials.

To end this FABULOUS day, we were given an assignment that is on Pg. 108 # 1-6, 8-9 in our 40S Applied Math Textbook. Following this were 2 more sheets, Extra NPQ questions to help us understand the concept better, and a HAND-IN sheet about everything we have learned so far in this unit.

* If you have any questions, check out the blog, listen to the podcasts on edline, or ask ask ask!!*

Applied Math 40S – Stats Outcomes

These are the specific outcomes of this unit. (i.e. you need to be able to do all this by the end of the unit)

Tut 3-1 – Binomial Distributions

• Difference between mean, median , mode – how to calculate from data list and frequency table
  
• Determine a binomial distribution using binompdf command. Interpret results
  
• Identify a binomial and uniform distribution
  

Tut 3- 2 Standard Deviations

• Understand what standard deviation refers to
  
• Calculate mean and standard deviation of a binomial distribution
  

       and
  

• Interpret standard deviation (i.e what does it mean in that situation?)
  

Tut 3-3 Normal Distribution

• Properties of normal distribution – classify a distribution as normal or not
  
  • 68 – 95 – 99 rule
    
• Problems with a normal distribution (e.g Cadbury egg type problems)
  

  
   

Tut 3-4 Standard Normal Distribution

• Properties of standard normal distribution
  
• Calculate z-scores ( ) and interpret results (comparing data like SAT scores)
  
• Use ShadeNorm and InvNorm
  
• Problems with Standard Normal Distribution
  

Tut 3 -5 Normal Approximation to Binomial Distribution

• rule
  
• Solve binomial distributions questions with a normal approximation
  

Tut 3-6 Confidence Intervals

• Calculate 90 , 95 or 99 % confidence intervals
  
  • Use , , or 1PropZ-Int
    
• Interpret a confidence interval (Describe what it means)
  

  
   

 

 

 

binomial distribution

Today in class we learned the difference between uniform distribution: all the probabilities are the same, binomial experiment: has success or failure, binomial distribution: results of the experiment.
we went over how to find the binomial distribution.
1. [2nd] [vars] go to binompdf (0)
2. First number= trials [,] second number= probability of success on each trial [enter]
3. [sto->] [2nd] [2] to get L2 [stat] [enter]
4. [2nd] [y=] [enter] turn on the first graph, make sure you select a histogram graph, make frequency L2
5. [window] change window to what you need for that particular graph [graph]
** note : look over pages 98-102 and page 349 **
the following MUST BE TRUE to make it a binomial distribution:
1. The experiment consists of n identical trials
2. Each trial results in one of two outcomes: the outcomes are often called a "success" (S) and a failure (F)
3. Probability of a success on a single trial is equal to P and remains the same from trial to trial. The probability of a failure is Q=1-P
4. The trials are independent.
5. The random variable of interest is Y, the number of successes observed during n trials.

Mean, Median and mode

Today in our Applied Math class room we started our new unit. Stats & Variability was the topic that we went over. We started the class off by reviewing what the mean, median and mode meant and how to solve for them. Also we looked at a frequency list used for larger amounts of data.
_
To calculate for the MEAN( X ) we learned the following example:
34 40 36
36 38 38
32 36 36
42 34 44
In order to find the mean you add up the table above, and divide by how many numbers there are in the chart above. ex. 446/12=37.17

~
To calculate for the MEDIAN( X ) we learned the following:
Median means middle number, If the number of terms given is even then find the middle of the two given terms.
^
To calculate for the MODE( X ) we learned:
Mode means most common number. If a number appears more then once there is your answer. To figure out on the calculator if you are given a more challenging question then the steps you take are listed below.
[stat] [edit or 1] [enter your numbers into the chart and delete any unwanted 0's or numbers] [2nd] [quit]. [stat] [--> or calc] [1 or 1-var stats] [2nd] [1] [enter] [ the down arrow changes your terms]

NEVER use the 2-Var Stats button under stat/ calc

Matricies WYNK - What You Need to Know

This is the WYNK for Network and Transition Matrices

work period

So, today we had a work period. We were told that our matrices test is on Tuesday. Today we worked on a handout test review. We also had time to work on our unit project, food web. Yes also I beat Rebecka S. at rock paper scissors.

example question: Wendy drives an old car. if it starts easily today, the probability that it will start easily tomorrow is 0.9. if it does not start easily today, the probability that it will start easily tomorrow is oly 0.85. write the transition matrix for the situation.


also here is the answer for number 4

click here for the PDF of the notes from today

Network Problems

Today in class we learned how to solve network problems with Matrices. The textbook examples can be found on page 72. The work that was assigned can be found on page 76, numbers 1-6. The example used in the text book was as follows:

y=YellowKnife
I=Inuvik
NW=Norman Wells
RI=Rankin Inlet
W=Whitehorse


Y I NW RI W Y I NW RI W
y 0 1 1 1 1 o 1 1 1 1
I 1 0 1 0 0 = A= 1 0 1 0 0
NW 1 1 0 0 0 1 1 0 0 0
RI 1 0 0 0 0 1 0 0 0 0
W 1 0 0 0 0 1 0 0 0 0

*You can travel directly from Inuvik to Norman Wells, but you have to go through Yellowknife to get from Norman Wells to Rankin Inlet.

*This network can be summerized in a table or matrix. An entry of 1 indicates that direct travel from a given city to another is possible. The entry 0 indicates that direct travel from a given city to another is not possible. The order in which the cities are listed in the matirx does not matter as long as the order is the same vertically and horizontally.

Things that happened

Today things happened. the end.

We learned about initial probability matrix which is called Po and is ALWAYS A ROW MATRIX! These are used to calculate probability over time. In order for them to work we need to make a transition matrix which are always SQUARES. They are represented by the letter T. So the entire class today was about PoT. The forumula is Pn=Po*Tn. We also discused the value of going to the dentist/school.