Winter Break! ( = Take Home Test)

Have an amazing winter break! Enjoy some quality time with your family and friends; relax, rest, play, and have fun! Take this time to recharge your batteries as we inch closer to midterm exams!

Speaking of midterm exams....over winter break you must complete the take home test provided in class, or under the "Classroom Powerpoints and Assignments" link on the right! Be sure to get this done!  A few points...

• Be sure to show work for all questions marked with a **! For those questions, no work, no credit!
• Don't do this the night before!
• Take your time! Use your notes, textbook, and online resources to ace this thing! The more effort you put into this take home test the more you're preparing yourself for the midterm! 
• And of course, the more effort you put in, the better your test grade will be!
• This will most likely be our last big test grade of the quarter! (We may have one more, smaller test)
• Read carefully!
• Feel free to email/Remind me with questions--but I won't answer any questions on Monday, January 2nd!
• You will lose 10 points for each day this is late. No take home tests will be accepted after Thursday, January 5th. 

After break we'll start a new unit--methods of data collection! This unit will covers chapter 11, 12, and 13. We will finish chapters 11 and 12 leading up to the midterm, and then you will be teaching yourself chapter 13 (experimental design) with a big take home assignment. Of course we'll discuss this more after break.

So, if you want to get a head start after you finish your take home test, feel free to read chapter 11 (simulations)! 

I'm super pumped for break but I'll definitely miss you guys! Have an amazing holiday season! See you all next year! :)

Homework = Midterm Review!

There is no homework due tomorrow!

Today in class we finished up our test and looked at two applications together--if you were out today you'll do this tomorrow!

Tomorrow we'll do a couple more problems about matrices and row operations (in groups), and then we'll use the rest of the time to start our winter break take home test!

The winter break take home test is the start of our review for the midterm! Use your notes, Khan Academy, and your online textbook to do your best and earn an A! Be sure to have this when we return from break--no excuses!

You can find the winter break take home test under the "PDF Textbook and Classroom Assignments" link on the right!

And finally (and maybe most importantly), thank you all so much for handling the past two days responsibly! I'm proud of you guys and absolutely appreciate having students like you!

Almost there....

Thank you all so much for handling my absences with responsibility! Now that's some AP level stuff! Great job!

If you were out today you will have to finish your math test (if needed) and complete your vocab test in class tomorrow! Be ready!

• The period is only 31 minutes; if you don't think you'll be able to finish the vocab in 20ish minutes so that you have 10ish left over to look at your math, come by in the morning! You can stop by before 7:30 or during a lunch/study hall to finish your math test if you like!
• However, if you know your vocab, you should have enough time for both...

• Here's the vocab list to study...

• 3 questions: identify if two events are disjoint, independent, neither, or both
• Probability
• Law of Large Numbers
• Law of Averages
• Sample Space
• Complement
• Equally Likely
• Independence
• Disjoint/Mutually Exclusive
• Venn Diagram
• Tree Diagram
• Conditional Probability
• Intersection
• Union
• Random Variable
• Probability Model/Probability Distribution
• Shifting
• Rescaling
• Expected Value
• Standard Deviation/Variance
• Pythagorean Theorem of Statistics
• Geometric Probability
• Binomial Probability

If you are done with both of these already you will have the opportunity to start your winter break take home test in class (and do a stamp problem)! The take home test will be uploaded under the "Classroom Powerpoints and Assignments" link to the right (or email me for a copy)!

See you there!

Vocab Test Tomorrow!

Hi everyone! I miss you guys! I should be back tomorrow.

What did you think about today's test? Although it may have been annoying or frustrating or surprising that you had to take a test with a sub today, it was arguably our best prep so far for the AP Exam! The AP Exam will be just like today--a test where I'm not around and you're totally on your own! (That's why I still gave the test with a sub, for this authentic practice!)

Tomorrow we will have our probability vocabulary test! This should take roughly 20-25 minutes (max). You will then be able to use 10-15 additional minutes to finish your math test (if needed).

If you are out tomorrow b/c of principal's bingo or caroling, first and foremost, have fun! And second, be prepared for your vocab test on Thursday! (You'll also get any remaining time to work on your math test).

Thank you so much for being responsible and understanding while I've been out. Feel free to send any questions/comments/feedback about the past two days via email (carofano.fm@easthartford.org) or Remind!

And here's what's on the vocab test tomorrow:

• 3 questions: identify if two events are disjoint, independent, neither, or both
• Probability
• Law of Large Numbers
• Law of Averages
• Sample Space
• Complement
• Equally Likely
• Independence
• Disjoint/Mutually Exclusive
• Venn Diagram
• Tree Diagram
• Conditional Probability
• Intersection
• Union
• Random Variable
• Probability Model/Probability Distribution
• Shifting
• Rescaling
• Expected Value
• Standard Deviation/Variance
• Pythagorean Theorem of Statistics
• Geometric Probability
• Binomial Probability

Math Test Tomorrow!

First and foremost, I apologize for being out today; I (obviously) did not anticipate being sick and never intended to be out. However, I have the utmost confidence that you can all prepare yourselves to succeed on tomorrow's test. The key to success on tomorrow's test is preparation! Study, study, study! Give me your best effort through this math test and vocab test, and then you'll get a chance to rest!

Here's an outline of what's on the math test tomorrow: (chapters 14-17)

• Find probability of "at least __ successes" or "at most __ successes" using binomcdf(
• Find probabilities using "AND" (Remember our first expected value homework? There was a game where you could score 0, 1, or 2 points; the game was played twice and we had to find the probability a person scored a sum of 0, 1, 2, 3, or 4...I would study how we found each of these probabilities).
• Find an "at least one" probability (either by hand, as in chapter 14, or using binompdf)
• Find probabilities using a Venn Diagram--you will have to find the value for "the middle," or the overlap--look at your "soccer/basketball" example with a Venn diagram in your notes
• Find a basic normal model probability (using normalcdf)
• Find a conditional probability using a two-way (contingency) table
• Find a conditional probability with a Venn diagram context (look at the owning cats/dogs example on page 1 of our chapter 14/15 mid unit quiz)
• Find the standard deviation when combining random variables (remember, VARIANCES ALWAYS ADD!)
• Find basic probabilities using "AND," "OR," and "NOT." (Study the types of problems from your chapter 14 quiz about the spinner, or the roulette example from our chapter 14/15 mid-unit quiz)
• Find the probability that the first success occurs in the ___th spot (by hand or using geometpdf)
• Find the probability of an exact number of successes using binompdf
• Create/use a tree diagram to find "and" probabilities and to find conditional probabilities (study the pregnancy test example from our chapter 14/15 quiz)
• Find a probability "without replacement"
• Study the "committee" example from our chapter 14/15 mid-unit quiz
• Calculate probabilities to complete a probability model
• Calculate expected value
• Interpret expected value

And here's what's on the vocab test the following day:

• 3 questions: identify if two events are disjoint, independent, neither, or both
• Probability
• Law of Large Numbers
• Law of Averages
• Sample Space
• Complement
• Equally Likely
• Independence
• Disjoint/Mutually Exclusive
• Venn Diagram
• Tree Diagram
• Conditional Probability
• Intersection
• Union
• Random Variable
• Probability Model/Probability Distribution
• Shifting
• Rescaling
• Expected Value
• Standard Deviation/Variance
• Pythagorean Theorem of Statistics
• Geometric Probability
• Binomial Probability

Finally, here's the answers to your sub work:

2015 AP Scoring Rubric and Solutions (scroll down to #3)

2016 AP Scoring Rubric and Solutions (scroll down to #4)

MC 64: D
MC 77: A
MC 72: D
MC 79: Check this out for extra practice!
MC 29: Skip
MC 74: Skip
MC 27: E
MC 69: C (Find prob. the first defect is 1st, 2nd, or 3rd)
MC 71: Skip (C)
MC 57: Check this out for extra practice!
MC 68: C (Notice this asks for the expected outcome after 4 games!)
MC 33: B

Weekend HW!

This weekend please complete the geometric and binomial probability practice (worksheet) provided in class (with some multiple choice on top)!

Here are the homework answers so you can check:

1. A

2. B

3. B

Part 2:

a. 4.975

b. 0.0267

c. 3.398E-21 or 0

d. E(x) = 160.8 (skip standard deviation)

e. Yes, 800 is less than 10% of all Americans.

f. 0.10185

g. 3.801E-18 or 0

h. 4.101E-6 = 0.0000041

i. 0.9999985

j. 0.5497 (*You will need to subtract two binomcdf's here)

k. 0.6744

How about some extra credit HW? For extra credit (and more binomial/geometric practice), complete parts A and B of the Geometric/Binomial review problems provided in class! (It says "A. Calculating Geometric Probabilities" at the top.

• Complete parts A and B.
• Ignore part C, this is not covered on our test (and we don't need to know how to do this b/c we can always use binomcdf for these types of problems).
• On Monday in class we'll answer any questions and do some reviewing for the test! See you there!

And here are the extra credit answers so you can check--you have to show the work to earn the EC!

Part A:
1. 4
2. 2.86E-6 = 0.00000286
3. 0.9961
4. 0.0615

Part B:
1. 0.2014
2. 1.455E-11 or 0
3. 0.0016
4. 1.0981E-6 = 0.0000010981
5. 0.0528
6. 1.8E-5 = 0.000018
7. 0.9999
8. 0.818
9. 0.0528 (you will have to subtract 2 binomcdf's here)
10. 0.18198
11. E(x) = 1.5 (skip standard deviation)

Finally, here's the plan for our tests next week--read this information below, and consider your schedule! If you know you will not be here, then be sure to make time to make up your test BEFORE break! It will not be a good idea to make the test up when you return--do whatever you need to do so you don't have a test looming over your head after break! Just come talk to me!

• Goal: finish chapter 17 on Friday (I am available B, G, or H period to review)
• Monday
• probability review and chapter 17 wrap-up (I am available B or H period to study)
• Tuesday
• probability math test
• Wednesday
• probability vocab test (and some open-note multiple choice)
• Thursday (1/2 day)
• Students who have done both tests will use this time to start their winter-break take home test!
• Students who were out caroling (or just out) on Wednesday will do their vocabulary test on Thursday!
• If you are out Tuesday you WILL NOT have enough time to do the "math test'" on a half day, so you will have to make time to do the test after school Monday, during study hall on Monday/Tuesday/Wednesday, or after school Tues or Weds
• If you are out both Tuesday and Wednesday you will do the vocab test on the half day (Thursday) but will have to make time to do the math test (Monday?)
• If you are leaving next week and will be out all week, or the above scenarios don't work for you, please come talk to me about your situation outside of class! Be proactive/responsible!

Read This!

First and foremost, unfortunately I will not be available after school on Monday. I apologize for originally stating I was; you will be on your own to study for your test! Here's my availability in the coming days:

• I am available after school today or during B, G, or H period today
• I am available during B, G, or H period tomorrow. 
• I am available during B period or H period on Monday.
• (Test Tuesday).

Be sure to study independently, but also, one of the best ways to study is with your peers--form a study group, ask each other questions, help each other out--learning is a collaborative process!

Here's tonight's homework:

Page 398: 7, 9, 11, 13, 19

Finally, here's the plan for our tests next week--read this information below, and consider your schedule! If you know you will not be here, then be sure to make time to make up your test BEFORE break! It will not be a good idea to make the test up when you return--do whatever you need to do so you don't have a test looming over your head after break! Just come talk to me!

• Goal: finish chapter 17 on Friday (I am available B, G, or H period to review)
• Monday
• probability review and chapter 17 wrap-up (I am available B or H period to study)
• Tuesday
• probability math test
• Wednesday
• probability vocab test (and some open-note multiple choice)
• Thursday (1/2 day)
• Students who have done both tests will use this time to start their winter-break take home test!
• Students who were out caroling (or just out) on Wednesday will do their vocabulary test on Thursday!
• If you are out Tuesday you WILL NOT have enough time to do the "math test'" on a half day, so you will have to make time to do the test after school Monday, during study hall on Monday/Tuesday/Wednesday, or after school Tues or Weds
• If you are out both Tuesday and Wednesday you will do the vocab test on the half day (Thursday) but will have to make time to do the math test (Monday?)
• If you are leaving next week and will be out all week, or the above scenarios don't work for you, please come talk to me about your situation outside of class! Be proactive/responsible!

Read This! (Weds HW, Thurs HW, Next Week's Tests...)

Tonight, please complete the half sheet provided in class today (or below)! The homework answers are also provided in red on the image below so you can check!

1. First, read each question and label it as "binomial" or "geometric" (B or G) probability.
2. Then, calculate each probability!
1. Use any method that works but...
2. Try to use "geometpdf" and "binompdf" for practice!
3. Some helpful hints...
1. Question a was not covered in class today! Think about this...if 20.1% of Americans speak a language other than English at home, how many people do we think we'll survey until we actually find a person who speaks a language other than English at home?
1. If you want some more specific help, check out "The Geometric Model" on page 387 of your book, or look at the "Step-by-Step" example on page 389!
2. Questions b and c are very much like the 3 problems we did today in class! Use questions a-c from today's notes to help! Or check out the TI tips on page 389-390 (geometric) or page 393 (binomial)!
3. Question d--this is an extension of what we learned today in class--it's like 3 "part a's" from today's notes combined into one problem....OR means add, so we'll have to find some probabilities and add them...
4. Questions e and f are problems we've dealt with before, but now we can use the graphing calculator to do these more quickly (and hopefully more simply); many of us will probably do some subtraction here...think about what "numbers of successes" the question is asking for; then, think about what "numbers of successes" are NOT included; find those probabilities, and then subtract from 1!

And here's tomorrow (Thursday) night's homework--you can't do it all yet, but you can definitely get a head start!

Page 398: 7, 9, 11, 13, 19

Finally, here's the plan for our tests next week--read this information below, and consider your schedule! If you know you will not be here, then be sure to make time to make up your test BEFORE break! It will not be a good idea to make the test up when you return! That might mean staying after, coming during study hall, or coming before school even--do whatever you need to do so you don't have a test looming over your head after break!

• Goal: finish chapter 17 on Friday
• Monday
• probability review and chapter 17 wrap-up (I will also be after school on Monday to study for the test!)
• Tuesday
• probability math test
• Wednesday
• probability vocab test (and some open-note multiple choice)
• Thursday (1/2 day)
• Students who have done both tests will use this time to start their winter-break take home test!
• Students who were out caroling (or just out) on Wednesday will do their vocabulary test on Thursday!
• If you are out Tuesday you WILL NOT have enough time to do the "math test'" on a half day, so you will have to make time to do the test after school Monday, during study hall on Monday/Tuesday/Wednesday, or after school Tues or Weds
• If you are out both Tuesday and Wednesday you will do the vocab test on the half day (Thursday) but will have to make time to do the math test (Monday?)
• If you are leaving next week and will be out all week, or the above scenarios don't work for you, please come talk to me about your situation outside of class! Be proactive/responsible!

Two's Day HW!

Tonight, please complete the AP Multiple Choice that we started in class (or below)! This will be collected and graded, so be sure to get it done!
**For #2 (not multiple choice) you must apply the Normal model; I should have typed this in the context for #1 but did not!!**

If you were out today we did some AP Free Response and these AP multiple choice after our chapter 16 vocab quiz! So, for those of you who were out, get these MC done tonight! Then you'll have to make up the classwork and our vocab quiz!

Tomorrow in class we'll move on to our last chapter of probability--chapter 17! See you there!

And finally, here are all of the solutions to last night's homework to help you with any questions or struggles you may have had....

Tonight, please complete the following in your textbook:

Page 383: 23, 27ab, 31bc, 33de, 37

• For 23 look at your notes about shifting and rescaling (for parts a,b)
• For parts c-d, consider the Pythagorean Theorem of Statistics--remember, VARIANCES ALWAYS ADD! 
• You can also look at your "dog and cat" examples from Friday in class
• For 27ab and 31bc, more practice like the "dog and cat" examples and more Pythagorean Theorem of Stat! (did I mention that VARIANCES ALWAYS ADD?!)
• For 33de...
• First (part d) find the new mean and standard deviation of the total amount of cereal (like part a of today's bike example)
• Then, (part e), use the Normal model with this new mean and standard deviation! (like part b of today's bike example)
• For 37...
• First find the mean and standard deviation of the team's total time! (like part a of our bike example)
• Then, use the Normal model for part b!

We also have our chapter 16 vocab quiz to start class tomorrow--be sure to study! This all came up in class! The list is below:

• Probability Model/Probability Distribution
• Expected Value
• Variance (standard deviation, squared)
• Standard Deviation (informs us about how the outcomes of a prob. model fluctuate or vary)
• Random Variable
• Discrete Random Variable
• Continuous Random Variable
• Shifting
• Rescaling
• Pythagorean Theorem of Statistics (variances always add!)
• Disjoint/Mutually Exclusive
• Independent
• Probability

After our vocab quiz we'll do some classwork--some AP multiple choice and free response! Then, on Wednesday, it's on to chapter 17! See you there!

Weekend (and Monday's) HW!

This weekend please complete the "Expected Value, Variance, and the Normal Model" problems provided in class (or below)!

• For question 1 use the Normal model to find the probability a student scores under 65, or from 65 to 80, or between 80 and 90, or over 90--this is review! Use your chapter 6 notes or some (AP Stats Guy) videos about calculating percentiles under the Normal model!
• Next, questions 2-4 get into our "new stuff"--creating a probability model and using it to find, then interpret, expected value!
• On the back question 6 gets into some of the shifting/rescaling ideas we discussed...
• And finally, for question 7 you have to consider what we learned today--the Pythagorean theorem of Statistics! Remember, VARIANCES ALWAYS ADD!

And if you're feeling like getting ahead, here's Monday night's homework--this is mostly based on "combining random variables" and the Normal model--the stuff we started to learn today in class (and will work with more on Monday)!

Page 383: 23, 27ab, 31bc, 33de, 37

We will have our chapter 16 vocab quiz on Tuesday! (You will get the chapter 15 quiz back on Monday). Here's the list of chapter 16 vocab to study:

• Probability Model/Probability Distribution
• Expected Value
• Variance (standard deviation, squared)
• Standard Deviation (informs us about how the outcomes of a prob. model fluctuate or vary)
• Random Variable
• Discrete Random Variable
• Continuous Random Variable
• Shifting
• Rescaling
• Pythagorean Theorem of Statistics (variances always add!)
• Disjoint/Mutually Exclusive
• Independent
• Probability

Thursday HW!

Tonight please complete the following in your textbook--more problems like last night!

Page 382: 17, 19, 21

• Create a probability distribution
• Remember: read the question to determine what your "outcomes" will be
• For example, if the question asks us to find the expected number of children, then we want to list "number of children" as our outcomes!
• Then, calculate the probabilities of each outcome--that's the hard part!
• Finally, remember to show work when calculating expected value, but use your graphing calculator to actually calculate expected value (mean) and standard deviation!

Tomorrow we'll get back to work with shifting, rescaling, and combining random variables! We'll also bring back the Normal model a bit--see you there!

And remember, VARIANCES ALWAYS ADD! :)

Wednesday HW!

Tonight, please complete the following in your textbook (some expected value and variance practice)!

Page 381: 3 and 11, 5 and 13, 7, 15

• I grouped "3 and 11" because 11 just asks you to find the standard deviation for the probability distribution--use your graphing calculator to do so!
• (Same for 5 and 13)
• In questions 3 and 5 you will have to do some work to find the probabilities to create the probability distribution--these will be more difficult than 7 and 15
• This is like Tuesday's homework or today's classwork examples--you have to do some work to calculate probabilities, they are not directly given!
• In question 7 you are given the probabilities you need; you have to read the context and create a probability distribution showing the outcomes and probabilities
• In question 15 you are given the probability distribution--this is the easiest case scenario--and need to find expected value and standard deviation
• For all questions SHOW ALL WORK FOR EXPECTED VALUE!
• Use your graphing calculator to find the standard deviation and to check your answer for expected value!
• For calculator help read the yellow box on the bottom of page 372

If you're feeling ambitious, here's tomorrow night's homework (more expected value stuff):

Page 382: 17, 19, 21

**Number 3 is based on a deck of cards--if you're not sure, here's the composition of a deck...**

Deck of Cards:

• 52 total cards
• 26 red cards
• 13 hearts
• 13 diamonds
• 26 black cards
• 13 clubs
• 13 spades
• There are 4 of each numbered card, one per suit
• So there are 4 of each card 2-10
• 4 Jacks
• 4 Queens
• 4 Kings
• 4 Aces

Tuesday HW!

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

This gets into some new stuff--click on the images and read the red/blue steps provided--these explain to you how to approach this problem! You definitely need this! It would also be a really good idea to do the extension questions in blue--not only will you get extra credit, you'll be getting a little ahead and a little more prepared for this chapter!

Tomorrow we'll get back into chapter 16 and continue to discuss expected value and variance! See you there!

"Quest" Tomorrow....STUDY!

Tonight, STUDY! We have a MAJOR QUIZ (a quiz that's more like a test...a "quest" if you will...) tomorrow!

There are two parts to the quiz:

• Chapter 14/15 Vocab Section:
• Use your chapter 14 quiz to study! Also use your notes!
• Here's the vocab list:
• Sample Space
• Disjoint/Mutually Exclusive
• Independent
• Union
• Intersection
• Probability
• Sum of Probabilities
• Complement
• Equally Likely
• Conditional Probability
• Venn Diagram (a diagram used for events that overlap, or events that are not disjoint)
• Tree Diagram (a diagram used for a sequence of events that shows conditional probabilities)
• Independence Formula (we did not touch on this in class--the formula is P(B/A) = P(B) or P(M/N) = P(M)
• Law of Averages
• Law of Large Numbers
• Chapter 14/15 Math Section:
• This portion of the quiz will cover all of the math we've covered thus far! Use the following to study...
• Review your chapter 14 quiz (spinner context) from last week!
• Use the practice problems provided in class or below! (answers provided in parentheses)
• 
  

• Review your homework from the weekend! (Answers below)






• Finally, review your classwork from Friday (half sheet, binge drinking/accident context, and multiple choice)!

Weekend HW! (And Friday's Classwork if you were out or didn't finish...)

This weekend, please complete some more tree diagram practice--an insurance related example with wind damage, and an HIV testing example! 

• For the Gulf Coast example your first set of branches should refer to the wind speed--either it's over (>) than x mph, or the wind is less than (<) x mph
• Then, based on the wind speed, we have to determine if the water damage came from above or below...so our next set of branches should show "damage from above" or "damage from below"!
• The challenge with questions a-f will be recognizing which questions are conditional and which are not! Good luck!
• For the HIV Testing example, our first set of branches should show whether a person has HIV or not; the prevalence of HIV tells us the probability that someone has HIV...
• Then, regardless if a person has HIV or not, if they take this test they can test positive or negative (unfortunately our medical tests aren't perfect, so sometimes people get false positives--people who aren't ill actually test positive--or false negatives--people who actually are ill test negative)...
• So, our next set of branches should show the probability that a person tests + or tests - with the Oraquick test!
• The percents given about the Oraquick test tell us the percent (or probability) that the test is accurate--to decide if the probability goes with the + or - branch, think: if a person does have HIV, what would be accurate? + or -? If a person does not have HIV, what would be accurate? + or -?

Here are the homework questions if you lost yours, forgot it, or were out:

Friday's classwork is below--if you did not finish in class, you can complete any questions you didn't finish on separate paper! You must show all work and record your answer! If you're not sure which problems you didn't finish, do them all! This must be turned in Monday.

IF YOU WERE ABSENT YOU SHOULD WORK ON THIS CLASSWORK! If not, you'll have to do it all Monday night!

Classwork Questions:

Thursday HW!

Tonight, please complete the following in your textbook (these are the same problems that are on the handout I provided in class!):

Page 364-366: 35, 37, 39, 41, 45 (You can also do question 15 for a little extra credit if you like--you'll have to look in the book for it)

Here are the answers (from the back of the book) in case you're using the handout and don't have your book with you:

35.) a. No, the flight leaving on time and luggage making the connection are not independent; the luggage is more likely to make the connection if the flight is on time.
       b. 0.695

37.) 0.975

39.) a. No, absenteeism and shift worked are not independent; night shift employees are twice as likely to miss work, work, work, work, work. 
        b. 0.014

41.) 0.571

45.) 0.563

Tomorrow in class I will provide an answer key with all of the tree diagrams and work shown as well! After our stamp we'll be doing some practice--some AP FR and MC! See you there!

And don't forget--we have a big quiz coming up on Tuesday! Chapter 14 AND 15 Vocab, as well as all the math we've learned thus far!