Winter Break is Here!

First and foremost, enjoy your break! Rest up, relax, enjoy some time with friends and family, and have some fun! But also, do some AP Statistics.

You have two responsibilities this break:

1.) Over Winter Break you must complete the "Teaching Yourself Chapter 13 (Experimental Design)" assignment

• Read through the chapter and answer the "reading questions" provided
• Remember, these are your notes!
• Feel free to record this info in your notebook!
• I do not plan to collect and grade these this year
• The more effort/detail you put into this the better your notes will be and the better prepared you'll be when we come back!
• The bold words serve as your vocab list--we will have a chapter 13 vocab quiz the Thursday after break.
• Then, use these notes and what you learned to answer the 25 multiple choice questions provided!
• These will be collected and graded the day you return as a quiz grade
• These are the types of MC questions we can see on the AP exam or on our midterm!
• If you need a copy of the winter break assignment you must email me  and I will send you the assignment. (carofano.fm@easthartford.org)

2.) Now is the time to start studying for your midterm! You need to email me over break and I will respond with a copy of the 2015 midterm exam for you to use to study!

• Email me @ carofano.fm@easthartford.org for the 2015 midterm exam--sending this email will be coutned as a homework grade! Do it as soon as you read this post!

• Midterm Exam Info:


• Free Response section (4 or 5 FR) = 60 minutes, 50% of your grade
• Multiple Choice (28 questions) = 60 minutes, 50% of your grade
• If you would like a copy of the 2015 midterm exam to study please send me an email and I will forward you a copy! I EXPECT ALL OF YOU TO EMAIL ME FOR THIS. (carofano.fm
• Chapters Covered:
• Unit 1 (Univariate Data): 2, 4,5,6
• Unit 2 (Linear Regression): 7,8,9,10
• Unit 4 (Probability): 14, 15, 16, 17
• Unit 3 (Data Collection): 13 (winter break project)
• Check out the image below for some suggestions about how to study:

3.) STAMPS are due the Thursday after break! Start counting now!

• Count your stamps!
• Write the total on the front! Double check!
• Your total must be correct! If I randomly select your name and double check your total and it's incorrect you will be given a 0 for your stamp grade.
• Get these all together--put them in a bag, an envelope, staple them--somehow get these all together
• If it's easier to rip a stamp off the corner of a paper than give the whole paper--do that! 

4.) If you are interested in taking an MCC class for credit please let me know ASAP!

• The course is MCC's "Math 138," or like our Math Modeling course
• This is a college algebra class--a lot of the stuff you learned in Algebra 2 and PreCalc 
• The course is taught by Ms. Beauchamp
• The class starts January 18th and ends May 10th
• Class is from 3:00-5:50 every Thursday
• You must provide your own transportation
• The class meets once a week so you must be highly responsible and do a substantial amount of work independently
• Grades will only be based on your quizzes and tests in class--your grade is only based on your ability/performance, not effort (it's a college class!)
• There are only 15 spots available
• Highly motivated students will be given first priority
• There is a permission slip! See me the day we're back!
• Or, email Joanna White (jwhite1@manchestercc.edu) if you have questions

One...more....probability homework...

Tonight please complete the binomial questions (the remaining questions) from last night's handout! Be sure to put in max effort into this hw and to check your answers (below) so that you are best prepared to ace tomorrow's classwork! 

Tomorrow in class we'll work with a partner (or two) on some binomial and geometric practice--and then it's on to our winter break!

For some more help with binomial probability and the calculator stuff check out the link below!

• Binomial Probability on the Graphing Calculator! Click Me! I'm a link!
• Or read the yellow box on page 393

Here are the homework answers so you can check: Bolded questions are binomial (tonight's hw)

Textbook Problems (pages 398-400):

• 7a.) 0.08192
• 7b.) 0.0064
• 7c.) 0.992

• 13a.) 0.0745
• 13b.) 0.5016(*Some lefties = not 0 lefties)
• 13c.) 0.211497
• 13d.) 0.01663
• 13e.) 0.01791
• 13f.) 0.99872

• 29a.) 5 people, on average
• 29b.) 0.06554

Frogs:

• a.) 0.20142
• b.) 0.0000173 (1.7295 E-5)
• c.) 0.08374
• d.) 0.182
• e.) 0.9887
• f.) 0.1333
• g.) 0.99821

Here are the homework questions in case you lost yours or were absent:

You can also check out this link for some interesting stuff about blood types!

Blood Types Chart and Info: Click Me! I'm another link!

Wednesday HW!

ALL PROBABILITY MAKEUP--QUIZZES, CLASSWORK, HOMEWORK, AND/OR TODAY'S TEST--MUST BE MADE UP BEFORE BREAK!

• Check your grade in PowerSchool to see what's missing!
• You may have 0's for homeworks that you didn't show me if you were absent on certain days!
• Probability unit ends Friday!
• Any work that is not made up before break will be (permanently) entered as a 0 (unless there is some extenuating circumstance that you discuss with me before then)
• You can make up any outstanding quizzes after school Wednesday or Thursday, or come during any free period/lunch.

Tonight's (Wednesday) HW: Please complete the geometric probability questions on the worksheet provided in class or below:

• Remember, geometric = "first"--part of the homework challenge is to recognize which questions are geometric probabilities!
• Questions:
• 7abc, 13ac, 29ab
• Back (frogs): c, f

Tomorrow's homework (last probability HW!) will be to complete the rest of the worksheet and calculate the binomial probabilities.

• If you'd like to get a head start and teach yourself some binomial probability check out the bullets below!
• To calculate binomial probabilities using our calculator check out the link below--this is what we'll discuss in class tomorrow!
• Binomial Probability on the Graphing Calculator! Click Me! I'm a link!
• Or read the yellow box on page 393

Here are the homework questions in case you lost yours or were absent:

Check out the link below for some interesting stuff about blood types!

Blood Types Chart and Info: Click Me! I'm another link!

Tomorrow in class we will discuss how to learn how to calculate binomial probabilities, and then on Friday we'll end the week with some classwork about binomial and geometric probabilities--which will be collected and graded as a "mini test grade!" See you there!

Weds HW (I'm def checking it...)

ALL PROBABILITY MAKEUP--QUIZZES, CLASSWORK, HOMEWORK, AND/OR TODAY'S TEST--MUST BE MADE UP BEFORE BREAK!

• Check your grade in PowerSchool to see what's missing!
• You may have 0's for homeworks that you didn't show me if you were absent on certain days!
• Over our winter break we will have an assignment that challenges us to teach ourselves about the new unit, collecting data, specifically with experiment design
• Probability unit ends Friday!
• Any work that is not made up before break will be (permanently) entered as a 0 (unless there is some extenuating circumstance that you discuss with me before then)
• You can make up any outstanding quizzes after school Wednesday or Thursday, or come during any free period/lunch.

Tomorrow we start our last chapter of probability--Geometric and Binomial probability (chapter 17)! This is ultimately going to involve a lot of new graphing calculator stuff, so be sure to bring it tomorrow!

Tonight please complete the "Intro to Geometric and Binomial Probability!" worksheet provided in class (or below)! 

• Answers are provided in () after each question--your job is to figure out the correct work!
• We don't really need to know anything new for the Geometric Probabilities in a-c...
• Just picture using "lines and words" and you got this! 
• Then, try to jump to some exponential forms of these answers!
• For d, try to use some proportional reasoning!
• OR you can look up the formula for expected value for geometric probability (but that's less interesting)
• The binomial probability stuff is tougher...
• For any "exactly" question we have to consider the number of possible ways to arrange "x successes" in "n trials..."
• To determine this we can use a formula, or our graphing calculator...
• For example, on question f, if I want to find the probability that exactly 2 of 5 people speak a language other than English at home I need to consider how many different ways I could have 2 people "speak a language other than English at home" with 5 total people
• I could try to list out all the ways (there are 10)
• Or I can use my calculator:
• Enter the # trials (5)
• Press MATH-->PROB-->choose nCr
• Enter the "# of successes" (2)
• Press enter
• Or, read pages 390-391 and look at the formula on the bottom of page 391
• For "at least," "at most," or between questions we have a cumulative probabilities....these will be tougher, but we do know the skills needed to figure these out
• For an easier way to calculate binomial probabilities using our calculator check out the link below:
• Binomial Probability on the Graphing Calculator
• Or read the yellow box on page 393

The more you can figure out tonight the more prepared you'll be as we discuss all this stuff in class tomorrow! See you there!

And here's the homework in case you were out or lost yours:

TEST TOMORROW!

We have our chapter 14-16 probability test tomorrow!

The best way to study is to do practice problems--you have a lot of those to choose from! 

1.) Work on the (17) probability review multiple choice questions provided in class on Friday (or below)!

• Don't worry too much about #10, there isn't anything like that on our test.
• The probability MC reviews many of the concepts we'll see on on our test!
• Check your answers!
• MC Review Answer Key:
1. D
2. D
3. A
4. A
5. D
6. A
7. C
8. B
9. C
10. D
11. E
12. B
13. A
14. D
15. A
16. E
17. D

2.) It would also be a good idea to try #37 and 38 on page 384 to make sure your comfortable with the combining random variables/Normal model stuff we worked with last week! These questions are also on the back of the #33 example we did in class Friday!

•  Answers:
• 37a) Mean = 200.57 seconds, Standard Deviation = 0.4619 seconds
• 37b) Probability of team beating its time = 0.00901
• "This team is not likely to swim faster than this time (199.48 seconds) because the probability of doing so is low (less than 1%)."
• 38a) Mean = 37.6 min, Standard Deviation = 3.6797 min
• 38b) I do not think the bike will be ready and set up as promised; the probability the bike is ready and set up in at most a half hour is only 0.01944.

3.) Another great way to study is to look over your previous quizzes!

• Look over your (two) chapter 14 quizzes (one take home, one in class) and your chapter 15 quiz!

4.) If you want some more practice/review to study for the test, check out the following in your textbook (and check your answers in the back of the book!)

• Page 384 (chapter 16): 37
• Page 402-407 (Review of Part IV = Probability Review):
• 3abc, 5, 7ab, 9a, 13b, 21, 31, 35, 37, 41

5.) Finish the "Combining Random Variables" AP multiple choice that we started today in class! 

• Here are the answers:
• 1.) D
• 2.) 0.12043 (your answer may be slightly different depending on how you rounded)
• 3.) C
• 4.) B
• 5.) B
• 6.) E
• 7.) C
• 8.) D
• 9.) D

6.) Try the "Juana and Carroll" free response question provided in class!

• Here are the answers:
• a.) Both expected values = 17.7
• If Juana and Carroll repeatedly play this game both are expected to score an average of 17.7 points per game, based on these probability models.
• b.) P(J16 and C17) = 0.045, P(J17 and C18) = 0.12, P(J18 and C19) = 0.06
• c.) 0.225
• d.) P(J-C = -2) = 0.085 (remember, probabilities must sum to 1)
• e.) 0.325
• Remember, this model is for the difference, "J-C." If Carroll is going to have a greater score than Juana, think about what type of difference 

7.) Complete the 2012 Free Response (on the back of Juana and Carroll)

• Here are the answers:
• a.) (Probabilities in order from left to right): 6/10, 3/10, 1/10 (or .6, .3, .1)
• b.) E(x) = $0.70 (*Remember to show work for this type of question)
• c.) 715 plays
• d.) 0.984435

Here are the probability review MC in case you lost yours or were absent:

Weekend = Study!

There is no formal homework to be checked Monday, but you should definitely use some time this weekend to start preparing for our probability test Tuesday (chapters 14-16)!

The best way to study is to do practice problems--this weekend you should complete the 17 probability review multiple choice provided in class (or below) to prep for our test! The answers are also provided below so you can check! 

It would also be a good idea to try #37 on page 384 to make sure your comfortable with the combining random variables/Normal model stuff we worked with today! 

• The probability MC reviews many of the concepts we'll see on Tuesday!
• Another great way to study is to look over your previous quizzes!
• You'll get your chapter 15 quiz back Monday, I apologize for not having it sooner
• Feel free to send me Remind messages if you have any questions on the review MC!
• Check your answers!
• MC Review Answer Key:
1. D
2. D
3. A
4. A
5. D
6. A
7. C
8. B
9. C
10. D
11. E
12. B
13. A
14. D
15. A
16. E
17. D
• If you want some more practice/review to study for Tuesday, check out the following in your textbook (and check your answers in the back of the book!)
• Page 384 (chapter 16): 37
• Page 402-407 (Review of Part IV = Probability Review):
• 3abc, 5, 7ab, 9a, 13b, 21, 31, 35, 37, 41
• I will be after school on Monday if you would like to come by to study!
• Work on the review MC and/or textbook problems below
• Ask any questions about these
• Practice, practice, Practice!

On Monday we'll focus on some more "chapter 16 stuff," and do some AP MC/FR with combining random variables in preparation for Tuesday's test.

Finally, here are the probability review MC in case you lost yours or were absent:

Thursday HW:

Tonight please complete the following in your textbook--this gives us some practice with finding the expected value (mean) and standard deviation when combining random variables.

Page 383: 25, 27ab, 31bc, 33

• Question #25 gives us some practice with the arithmetic of shifting/rescaling (a-d) and then combining random variables (part e).....
• Questions 27ab and 31bc are based on the ideas we discussed today with the dogs and cats...
• Question 33
• Start with 33d and e
• 33d asks us to find the mean and standard deviation of the total amount of cereal in the two bowls, which is based on our learning today (cats and dogs)
• 33e then challenges us to use this new mean and standard deviation to find a probability with a Normal model--you got this!
• Then go to 33ab...
• 33ab are again referring to combining random variables--back to cats and dogs....
• 33c is definitely the hardest homework question....we're using the Normal model again....good luck!

Tomorrow in class we'll discuss #33 and then look at some more examples with combining random variables (and the Normal model)! Then we'll do some studying this weekend and some classwork/practice on Monday! See you there!

Here'sthe outline of our course through midterm exams:

Wednesday (12/13) = Recap of creating probability models and finding expected value (homework questions/review), then discussion of shifting/rescaling random variables

Thursday (12/14) = Combining Random Variables notes/examples (Pythagorean Theorem of Statistics!)

Friday (12/15) = More Combining Random Variables!

Monday (12/18) = Finish chapter 16 and answer probability questions--classwork/practice

Tuesday (12/19) = Probability Test: Chapters 14, 15, 16

Wednesday (12/20) to Friday (12/22) = Geometric and Binomial Probability (mini-test Friday 12/22?)

Winter Break = "Teaching Yourself Chapter 13--Experimental Design" Project

Tuesday (1/2) to Friday (1/5) = Recapping Experimental Design (notes/discussion/AP MC and FR)

Monday (1/8) to Friday (1/12) = Midterm Exam

When's Day HW!

Tonight please complete the AP MC provided in class (or below)!

• I'm a moron and accidentally put the same question twice (#'s 5 and 6)! Sorry about that!
• Remember, any time you want some expected value, first create a probability model!

Tomorrow in class we'll have a stamp problem dealing with shifting and rescaling random variables; then we'll start to look at combining random variables and begin to explore the Pythagorean Theorem of Statistics (sounds fancy)! See you there!

Here's the outline of our course through midterm exams in case you're curious...

Wednesday (12/13) = Recap of creating probability models and finding expected value (homework questions/review), then discussion of shifting/rescaling random variables

Thursday (12/14) = Combining Random Variables notes/examples (Pythagorean Theorem of Statistics!)

Friday (12/15) = More Combining Random Variables!

Monday (12/18) = Finish chapter 16 and answer probability questions--classwork/practice

Tuesday (12/19) = Probability Test: Chapter 14, 15, 16

Wednesday (12/20) to Friday (12/22) = Geometric and Binomial Probability (mini-test Friday 12/22?)

Winter Break = "Teaching Yourself Chapter 13--Experimental Design" Project

Tuesday (1/2) to Friday (1/5) = Recapping Experimental Design

Monday (1/8) to Friday (1/12) = Midterm Exam

Two's Day HW!

Tuesday night's homework is in the book--but these are the same problems that are on the handout I gave you in class! The answers are also posted below.

Page 381-383: 3/11, 5/13, 7, 15, 21

• The problems are written as 3/11 b/c #11 asks for the standard deviation of the probability model created in #3 (same for 5/13)
• To find standard deviation we will simply use our calculator (we can also use our calculator to find E(x))
• Check out the yellow box on page 372 to see how to use your calculator to find expected value and standard deviation
• For 3, 5, and 21 the hardest part of the question will likely be calculating the probabilities for our probability model! This requires us to consider all of the skills we learned in chapters 14/15!
• Here are the questions:

• And here are the answers:
• 3a) Amount Won:     $0           $5            $10            $30   
•       Prob                   26/52      13/52         12/52        1/52
• 3b) $4.13 won per play (on average)
• 3c) $4ish
• 11) $5.44
• 5a) Children              1              2            3
•        Prob                0.50          0.25       0.25
• 5b) 1.75 children per family (on average)
• 5c) 0.87 boys per family (on average) (create a new probability model for the # of boys first)
• 13) 0.83
• 7) $27,000 (on average)
• 15a) 1.7 calls per hour (on average)
• 15b) 0.9
• 21a) # Good Batteries      0          1             2
•           Probability            0.067    0.467      0.467
• 21b) 1.40 good batteries (on average)
• 21c) 0.61        

Here's the outline of our course through midterm exams in case you're curious...

Thursday (12/7) = Chapter 15 Vocab Quiz, Tree Diagram Practice (HIV Testing, Hurricane Katrina)

Friday (12/8) = Chapter 15 Classwork (AP MC and FR)

Monday (12/11) = Start chapter 16!

Tuesday (12/12) = Chapter 15 Quiz (15 min) and Chapter 16 Notes

Wednesday (12/13) to Friday (12/15) = Rest of Chapter 16, Chapter 16 Vocab Quiz and Classwork

Monday (12/18) = Finish chapter 16 and answer probability questions

Tuesday (12/19) = Probability Test: Chapter 14, 15, 16

Wednesday (12/20) to Friday (12/22) = Geometric and Binomial Probability (mini-test Friday 12/22)

Winter Break = "Teaching Yourself Chapter 13--Experimental Design" Project

Tuesday (1/2) to Friday (1/5) = Recapping Experimental Design

Monday (1/8) to Friday (1/12) = Midterm Exam

Monday HW!

Tonight please complete the "Uncovering Expected Value" worksheet provided in class (or below).

• Usually with these types of problems the hardest part is creating the probability model
• Check out the image below--everything written in red is a "hint" to help with your homework in case you get stuck!
• You can also check your probabilities--the correct probabilities are in the table below!
• For #6, Interpret Expected Value, use this structure:
• "Based on the probability model, if we repeatedly _______________, we expect to ______________________. 
• Check out this question in the image below!

Also, remember that we have our chapter 15 quiz to start class tomorrow! Look over your weekend homework and today's stamp to study!

After our quiz tomorrow it's back to work on chapter 16 (random variables)--see you there!

Here's tonight's HW in case you lost yours or were out:

Tuesday night's homework will be in the book--if you like, here's the assignment so you can get a head start:

Page 381-383: 3/11, 5/13, 7, 15, 21

• The problems are written as 3/11 b/c #11 asks for the standard deviation of the probability model created in #3 (same for 5/13)
• To find standard deviation we will simply use our calculator (we can also use our calculator to find E(x))
• Check out the yellow box on page 372 to see how to use your calculator to find expected value and standard deviation
• For 3, 5, and 21 the hardest part of the question will likely be calculating the probabilities for our probability model! This requires us to consider all of the skills we learned in chapters 14/15!

Here's the outline of our course through midterm exams in case you're curious...

Thursday (12/7) = Chapter 15 Vocab Quiz, Tree Diagram Practice (HIV Testing, Hurricane Katrina)

Friday (12/8) = Chapter 15 Classwork (AP MC and FR)

Monday (12/11) = Start chapter 16!

Tuesday (12/12) = Chapter 15 Quiz (15 min) and Chapter 16 Notes

Wednesday (12/13) to Friday (12/15) = Rest of Chapter 16, Chapter 16 Vocab Quiz and Classwork

Monday (12/18) = Finish chapter 16 and answer probability questions

Tuesday (12/19) = Probability Test: Chapter 14, 15, 16

Wednesday (12/20) to Friday (12/22) = Geometric and Binomial Probability (mini-test Friday 12/22)

Winter Break = "Teaching Yourself Chapter 13--Experimental Design" Project

Tuesday (1/2) to Friday (1/5) = Recapping Experimental Design

Monday (1/8) to Friday (1/12) = Midterm Exam

Excellent work today in class! We had some tough AP MC as well as a difficult AP FR (2017) in class--I'm impressed with how well we did! Let's carry that positive momentum into next week and the week after! Two more weeks of maximum effort before break!

Weekend Homework: Please complete the probability review questions provided in class (or below)!

• Complete each question on separate paper
• THIS ASSIGNMENT WILL COUNT DOUBLE
• This means I'm DEFINITELY CHECKING homework Monday--I know there were a couple assignments I didn't check this week, but I plan to get back to checking 99% of your homework....
• (The answers are provided in parentheses)
• This is a review of the fundamental skills we need thus far! This is also review for our (15 minute) chapter 15 quiz on Tuesday!

On Monday in class we will start our new stuff--Expected Value and Random Variables (chapter 16)! See you there!

Here's the outline of our course through midterm exams in case you're curious...

Thursday (12/7) = Chapter 15 Vocab Quiz, Tree Diagram Practice (HIV Testing, Hurricane Katrina)

Friday (12/8) = Chapter 15 Classwork (AP MC and FR)

Monday (12/11) = Start chapter 16!

Tuesday (12/12) = Chapter 15 Quiz (15 min) and Chapter 16 Notes

Wednesday (12/13) to Friday (12/15) = Rest of Chapter 16, Chapter 16 Vocab Quiz and Classwork

Monday (12/18) = Finish chapter 16 and answer probability questions

Tuesday (12/19) = Probability Test: Chapter 14, 15, 16

Wednesday (12/20) to Friday (12/22) = Geometric and Binomial Probability (mini-test Friday 12/22)

Winter Break = "Teaching Yourself Chapter 13--Experimental Design" Project

Tuesday (1/2) to Friday (1/5) = Recapping Experimental Design

Monday (1/8) to Friday (1/12) = Midterm Exam

And lastly, one of our classmates lost a necklace that's very important to them--if you see this necklace anywhere (including on a person) please let me know!

Thursday (and weekend) Homework!

Tonight please complete the following problems from your textbook--these are the same problems that are on the printout provided in class!

Page 366: 35/37, 39/41, 43, 45

• This homework assignment gives us another night of practice with all this conditional probability and tree diagram stuff!
• Here are the answers so you don't have to use your book (you'll also get a key tomorrow with all of the work shown)....
• 35a) No, leaving on time and the luggage making the connection are not independent; the luggage is more likely to make the connection if the flight is one time (the probability is higher).
• 35b) 0.695
• 37) 0.975
• 39a) No, absenteeism is not independent of shift worked; the probability of being absent for night employees is double that of employees on the day shift.
• 39b) 0.014 = 1.4%
• 41) 0.571 = 57.1%
• 43a) 0.20
• 43b) 0.272
• 43c) 0.353 
• 43d) 0.033
• 45) 0.563

This weekend you will have a "probability review" homework assignment that recaps many of the ideas we've covered so far (a little studying after two chapters). If you're feeling crazy and want to get a head start tonight, here are the problems:

Tomorrow in class we'll do a bunch more AP problems (MC and FR) that will be collected and graded as classwork! See you there! 

And here's the outline of our course through midterm exams in case you're curious...

Thursday (12/7) = Chapter 15 Vocab Quiz, Tree Diagram Practice (HIV Testing, Hurricane Katrina)

Friday (12/8) = Chapter 15 Classwork (AP MC and FR)

Monday (12/11) = Start chapter 16!

Tuesday (12/12) = Chapter 15 Quiz (15 min) and Chapter 16 Notes

Wednesday (12/13) to Friday (12/15) = Rest of Chapter 16, Chapter 16 Vocab Quiz and Classwork

Monday (12/18) = Finish chapter 16 and answer probability questions

Tuesday (12/19) = Probability Test: Chapter 14, 15, 16

Wednesday (12/20) to Friday (12/22) = Geometric and Binomial Probability (mini-test Friday 12/22)

Winter Break = "Teaching Yourself Chapter 13--Experimental Design" Project

Tuesday (1/2) to Friday (1/5) = Recapping Experimental Design

Monday (1/8) to Friday (1/12) = Midterm Exam

And lastly, one of our classmates lost a necklace that's very important to them--if you see this necklace anywhere (including on a person) please let me know!