Happy Holidays!

Have an amazing break! I won't see you all until January 7th, so it'll be a while, and I definitely will be excited to see you all when I'm back!

Over break, there is no formal assignment--but start studying for your midterms!

• There is an outline of the midterm exam topics (all of the stuff on the test) under our classroom resources link. It's right at the top, entitled, "2016 Midterm Exam Topics."
• There is also a link for some different ways to study for the midterm and/or AP exam (I gave you this in class)
• The date of our AP Exam is incorrect on the paper I gave you today--our AP exam is Thursday, May 12th, 2016.
• We will have two midterm review assignments (with a sub) when we come back from break, so if you do some studying over break it will make those assignments a little easier!

Here is the plan for when you have the sub on Monday/Tuesday after break:

• Monday: The sub should give you a packet of questions; on the front is a 2009 Free Response question (with a boxplot); then, there is a question regarding linear regression (mass v. rate) and a paper where you have to create some histograms boxplots.
• You should do your best to finish this in class (you should be able to finish most of it); whatever you do not finish should be completed for homework. 
• Tuesday: The sub should give you a multiple choice packet that says, "AP Statistics Take Home Exam: Happy Thanksgiving!" at the top. These are practice multiple choice questions for the midterm. Do as much as you can in class, and then complete the rest for Thursday. 
• Ultimately, both assignments need to be fully completed for Thursday. Bring both with you to class on Thursday and we'll use them as a starting point for some questions/review.

Other than that, enjoy your break! Rest up, relax, spend some time with friends and family, and recharge your batteries! We have a midterm exam soon after we're back, and then it's the final push toward our AP exam!

See you all in a couple weeks!

(My Christmas jams...)

Oh, and here's the stamp problem in case you didn't get to it on Thursday (you can get 3 stamps!)

Stamp: Answer each question below thoughtfully:

1.) If you could give one gift to any person in the world, who would you give it to and what would you give?

2.) If you could receive any gift (that costs less than $1,000), what would it be?

3.) Suppose I hand you one gift, a wrapped box. Would you rather take a gift, or give a gift? Why?

Stamps will be due on exam day (or earlier). We will not have any more stamps for this quarter, so feel free to get those counted up and put together over break! (You can give yourself the 3 stamps for this if you did it).

Vocab Test Tomorrow!

Tonight, study your vocab! Remember, you will potentially have some additional time to work on today's test (in a different color...) after your vocab--but the amount of extra time you have will depend on how quickly you can finish the vocab test! So study! The better you know the definitions, the quicker you'll finish!

Here's a list of what's on the vocab test (tomorrow):

• Probability
• Random Variable
• Pythagorean Theorem of Statistics
• Independence
• Law of Large Numbers
• Law of Averages
• Venn Diagram
• Tree Diagram
• Bernoulli Trial
• Binomial Probability
• Geometric Probability
• Complement
• Expected Value
• Conditional Probability
• Disjoint/Mutually Exclusive
• Probability Model
• Variance/Standard Deviation
• Intersection 
• Union
• Sample Space
• Equally Likely

TESTS!

Tomorrow we have our probability test (chapters 14-17)! Here's a list of what's covered:

• Binomial Probability: (chapter 17)
• At least, at most, and between questions (binomcdf)
• "Exactly" questions (binompdf)
• Find expected value, standard deviation for a binomial model
• Find probability of "at least one" (chapter 14 and chapter 17)
• Calculating probabilities for events that overlap: Venn diagrams (ch. 15)
• Calculating conditional probabilities (ch. 15)
• With tree diagrams
• With contingency or two way tables
• Given a table or given probabilities
• Calculating probabilities with the Normal model (ch. 6/ch. 16)
• Finding new expected value, standard deviation, variance, when combining random variables (ch. 16)
• Pythagorean Thm. of Statistics
• Calculating "basic" probabilities using words, and, or (ch. 14)--like our spinner or blood type ch. 14 quiz
• Geometric probabilities (ch. 14/ch. 17)
• Find probability that the first success it the ___th spot
• Calculating probabilities without replacement (ch. 15)
• Using tree diagrams to model scenarios and calculate probabilities (ch. 15)
• Expected value and standard deviation of a probability model (ch. 16)
• Create probability model
• Find expected value (show work)
• Find standard deviation (on calc)
• Use expected value to make decisions

Here are the answers to the review multiple choice (from class today) so you can use them to check your work and study!

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

And lastly, here is the vocab list for Wednesday's probability vocab test:

• Probability
• Random Variable
• Pythagorean Theorem of Statistics
• Independence
• Law of Large Numbers
• Law of Averages
• Venn Diagram
• Tree Diagram
• Bernoulli Trial
• Binomial Probability
• Geometric Probability
• Complement
• Expected Value
• Conditional Probability
• Disjoint/Mutually Exclusive
• Probability Model
• Variance/Standard Deviation
• Intersection 
• Union
• Sample Space
• Equally Likely
• Shifting
• Rescaling
• Discrete Random Variable
• Continuous Random Variable

Weekend HW/Next Week Schedule

This weekend...

1. please complete the chapter 17 classwork that we started in class. (You can also find it below if you were out--if you do this, you're caught up). The answers are also posted below so you can check your work.
2. Please complete the Chapter 17 Vocab Quiz. This will be collected/graded on Monday. Use your notes and get an A!

Here's the classwork if you were out:

And here are the answers:

Next week:

• Monday: probability review/study for Tuesday's test
• Tuesday: probability (math) test!
• Wednesday: probability vocab test! (list below...)
• Probability
• Random Variable
• Pythagorean Theorem of Statistics
• Independence
• Law of Large Numbers
• Law of Averages
• Venn Diagram
• Tree Diagram
• Bernoulli Trial
• Binomial Probability
• Geometric Probability
• Complement
• Expected Value
• Conditional Probability
• Disjoint/Mutually Exclusive
• Probability Model
• Variance/Standard Deviation
• Intersection 
• Union
• Sample Space
• Equally Likely
• Shifting
• Rescaling
• Discrete Random Variable
• Continuous Random Variable

Thursday HW!

Tonight, please complete the binomial/geometric probability practice provided in class (or below)!

Wednesday HW

Today was our last full Wednesday AP Stat class until January 20th! Whatttttt?!

Tonight, please complete the following in your textbook:

Page 398: 1, 7, 9, 13abcd, 15a

Tomorrow in class we'll finish our notes on geometric/binomial probability...then, we'll practice on Friday and start getting ready for our test!

Vote on the poll (top right corner of the blog) to determine when our vocab test is! The poll will close Thursday at midnight!

Tuesday HW = Chapter 16 Take Home Quiz!

Tonight, please complete the chapter 16 take home quiz provided in class (or below).

• This will be collected and graded as a quiz, so don't forget!
• Use your chapter 16 notes and the textbook for help!
• SHOW ALL WORK! 
• Except #2--you can do #2 using your calculator (since it's multiple choice), so you may not show work here

Tomorrow in class we'll get into the math of chapter 17; then, we'll practice on Thursday/Friday/Monday, and it'll be test time on Tuesday! Do all of your homework!

Monday HW!

Tonight, please complete the two free response questions provided in class (2015 #3 and 2005 Form B #2).

This will count as a double homework--so do it! I'm checking!

If you need the first homework question click here (scroll down to question #3)

If you need the other homework question click here! (scroll down to find question #2)

Want a little homework extra credit?

1. Use the AP scoring rubrics (linked below) to score your responses!
2. You must jot a couple notes down about why you gave yourself each score (even if it's an E); no notes, no extra credit!
3. If you score both AP free response and jot notes for both, you can get credit for an "extra" homework! 
• 2005 Form B Scoring Guidelines and Rubric (look for #2)
•  
• 2015 Scoring Guidelines and Rubric (scroll down to question 3)

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

Weekend HW!

This weekend, please complete the following in your textbook:

Page 382: 17, 21, 33, 37

• Questions 17 and 21 deal with expected value and standard deviation, and creating a probability model--some of the stuff we learned about earlier this week
• Questions 33 and 37 deal with combining random variables and the Pythagorean Theorem of Statistics (Friday's notes)
• This also brings back the Normal model! 37 is tough! Do your best and use the answers from the back to figure it out (if you need to)!

Vocab Quiz Monday (Chapter 16): 

• Expected value
• Variance
• Probability model
• Random variable
• Discrete random variable
• Continuous random variable
• Standard deviation
• Shifting
• Rescaling
• Pythagorean theorem of statistics

Finally, if you did not complete Thursday's homework (see the blog post below if you need it) you can show me Monday! Do it!

• For question 1 we need to use the Normal model--thus, z-scores and normalcdf(-- to find these probabilities
• Look at your chapter 6 notes, or we reviewed the Normal model with some notes (about IQ's or SAT's) earlier this week!
• You'll need to use normalcdf( to find the probability a student scores under 60, between 60 and 80, between 80 and 90, and over 90
• For example, to find the probability a student scores between 60 and 80, I find the z-score for 60 and 80 (they come out to be z = -2.5 and z = 0.83)
• Then, I use normalcdf to find the probability: normalcdf(-2.5, 0.833) = 0.7915
• This is all review for our exam! Figure it out!
• Question 2 then gets into the "new stuff," finding expected value and the standard deviation (of the probability model)
• For question 2, the probabilities are what you calculated in #1!
• The probabilities should be:
• Under 60 = $0: 0.00621
• Between 60 and 80 = $50: 0.7915
• Between 80 and 90 = $100: 0.19612
• Over 90 = $200: 0.00621
• Always make sure your probabilities sum to 1!
• For the remainder of the questions, it's all "new stuff" from this week (chapter 16)!
• Use your notes to figure it all out!
• 
  

Thursday HW

Tonight, please complete the "Expected Value, Variance, and the Normal Model" worksheet provided in class (or below).

Tomorrow in class we'll do some practice AP problems (in groups); then, on Monday we'll have our chapter 16 vocab quiz and do some more chapter 16 to wrap up! See you there!

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

Expected Value, Variance, and the Normal Model 

Suppose that on a classroom statistics test, the mean test score on the first exam was 75 and the standard deviation was 6 points. Further, a distribution of these scores proves to be unimodal and symmetric. Now, let’s suppose your teacher turns your next test into a sort-of “game show.” That is, he/she will pay you different sums of money for different scores. We will assume that students’ scores are a random variable and subsequent tests will reflect the Normal model of the first exam. The payout will break down as follows:

a.       Under 60 points: $0

b.      From 60 to 80 points: $50

c.       80 – 90 points: $100

d.      Over 90 points: $200

1.       Find the probability that each score falls within the ranges identified above. (Hint: when we need probabilities or proportions under a Normal curve, where do we have to look?) You should list your four answers clearly, and show all work in the calculation of each.  (4 points)

2.       Using your answers from (1) above, create a probability distribution for the expected amount of earnings after the upcoming test. (Your table should include a column for each outcome ($) and its probability). (2 points)

3.       Find the expected value and variance of your earnings from the test. (Remember variance is standard deviation, squared!) (2 points)

4.       Interpret your expected value from (3) above in a complete sentence, in context. (2 points)

5.       After a few tests, your teacher is too broke from shelling out cash for students’ good scores. So, to continue this policy, he’ll need to collect some sort of fee for you to “play.”

a.       Based on your expected value, how much would you be willing to pay to play this sort of game with your test scores? Explain your reasoning in detail. (2 points)

6. If the teacher plans to quintuple each prize (multiply by 5), find the new expected value and variance. (2 points)
7. Suppose you were going to play this game three times and add your earnings each time. Find the expected value and variance for 3 consecutive plays. (2 points)

Wednesday HW

Tonight please complete the "Juana and Carroll" problem provided in class (or below)

Even if you were out today (but here yesterday) you can do this! So do it!

Tomorrow in class we'll finish up our chapter 16 notes and discuss how to combine random variables.
Then, on Friday, we'll do some AP problems...on Monday we'll wrap up chapter 16 with our vocab quiz and some more AP problems!

See you tomorrow! Enjoy your Wednesday!

Tuesday HW

Tonight, please complete the following in your textbook:

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

Remember, for each question where you're asked to find expected value (and/or standard deviation), you first need to create a probability model! (A table showing each possible outcome and the probability of each outcome). There's a good chance that the hardest part will be calculating the probabilities for this model!

Tomorrow we'll talk about homework and continue to work with expected value, and we'll start talking about combining random variables!

See you there! Happy Tuesday!

Monday: Back to the Grind!

Back to work!

Tonight, please complete the AP problem provided in class (or in blue below)! The homework answers are next to each question in pink.

Also, don't forget--if you any anything to make up (homework and/or quizzes--ALL MAKEUP HW/QUIZZES MUST BE DONE BY WEDNESDAY (or after school Weds.)!

AP Problem: Using Probability

Some golf balls are required to meet a set of five standards to be used in professional tournaments. One of these is the distance traveled. A ball hit by a mechanical device, Iron Byron, with a 10 degree angle of launch, a backspin of 42 revolutions per second, and a ball velocity of 235 ft/sec, should not exceed a distance of 291.2 yards. Companies hope to develop balls that will travel as close to this 291.2 distance as possible, without exceeding it. One manufacturer has determined the distances are normally distributed with a standard deviation of 2.8 yards. This manufacturer has a new process that allows it to set the mean distance the ball will travel.

1. Suppose the manufacturer sets the mean distance to 288 yards; calculate the probability that a randomly selected ball travels too far. (0.1265)
2. Suppose the mean distance is 288 yards and that five balls are independently tested. Calculate the probability that at least one of the five balls will exceed the max distance of 291.2 yards. (0.4915)
3. The manufacturer wants to be 99% sure a randomly selected ball will not exceed the maximum distance of 291.2 yards; what is the largest mean that can be used in the manufacturing process? (284.69 ft; first, you have to use invnorm( to find what z-score has 99% of the data below it. Remember, to do this, we go to invnorm( on our calculator; the "area" is the % to the left, or .99. For mu and sigma we want to enter 0 and 1 because we want a z score. Now, we know the z-score of 2.326 has 99% of the data below it. We can sub the z-score, x, and Sx into the z-score formula and solve for the mean to find this answer). 

Happy Weekend! (And Homework...)

This weekend, please complete the following:

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

**These are the same problems on the sheet I gave you today in class. (The sheet I gave you is just the problems from the booked typed up, so you don't have to carry your book maybe...)

Remember, all make up work--homework from when you were absent, missing quizzes, anything--is DUE BY WEDNESDAY. 

On Monday we'll get into some new stuff (and answer homework questions) from chapter 16--expected value and variance!

In case you aren't using your book (because I typed up the problems for you), here are the homework answers:

35.) a. No, the flight leaving on time and luggage making the connection are not independent, because the probability the luggage makes the connection is dependent upon whether the flight arrives on time (95% chance the luggage arrives if the flight is on time, 65% chance if it isn't on time).
b. 0.695

37.) 0.975

39.) a.) No, absenteeism is not independent of shift worked. It appears night shift workers are more likely to be absent (2% vs. 1%).
b. 0.014

41.) 0.571

43.) a. 0.2
b. 0.272
c. 0.353
d. 0.033

45.) 0.563

Vocab Quiz Tomorrow and HW!

     Tonight, please complete the worksheet provided in class with problems regarding binge drinking and graduating college. These problems are also below in case you lost yours or were out! (If you were absent and you can figure out this homework then you're caught up on what we learned today in class!)

  Also, remember we have our chapter 15 vocab quiz tomorrow! Study! Here's the list:

Sample Space
 Disjoint/Mutually Exclusive
 Conditional Probability(used when we know some information to be true)
 Independence
 OR (Union, Add)
 AND(Intersection, Multiply)
 Venn Diagram (used when we have an overlap between two events)
 Tree Diagram (used when we have multiple events occurring, shows conditional probabilities
 Probability
 Complement
 Equally Likely
Independence Formula (P(B/A) = P(B)) 

Wednesday/Thursday HW

Tonight, please complete the last two slides in your powerpoint (for your notes): (the problems are also listed below)

1. During one month, 88% of drivers filled up with regular gasoline, 2% middle grade, and 10% bought premium gas. Of those who bought regular gas, 28% paid with a credit card; 34% and 42%, respectively, paid with a credit card. For this question, first draw a tree diagram (the first event is "type of gas" with 3 branches, and the next event is "type of payment," which will have 2 branches (credit card or not credit card).
• What is the probability that the customer paid with a credit card?
• Remember, we multiply across the branches in our tree diagram. Think: which branches represent paying with a credit card? Find these (3) branches, and add these 3 probabilities from the "far right."
• What is the probability that someone who paid with a credit card bought premium gas?
• What is the probability that someone who did not use a credit card bought regular gas? 
• The second and third questions are both conditional probability. For both, think about "what you know to be true." For instance, in the second question we know the person paid with a credit card, or we're given "credit card." Now, think about and use your conditional probability formula! (You should have one number in the numerator, and 3 numbers being added in the denominator). 
2. A bag of names for a Secret Santa has 12 names; 8 are ladies and 4 are gentlemen. You will draw a name first, and then your sibling will draw. Remember, names are drawn without replacement. So for this question, I'd recommend using a tree diagram, but using fractions for our probabilities. The first part of our tree diagram represent what "you draw" (male or female); then, our second branch represents our siblings draw (also male or female). 

• What is the probability that you and your sibling draw opposite sexes? 
• Which branches represent drawing opposite sexes? Find these two branches and add these probabilities from the "far right."
• You haven’t opened up your name—it’s still folded in your hand. Your sibling drew a male’s name. What is the probability that you also drew a male?
• Here, we know our sibling drew a male, so we have conditional probability ("given sibling drew male"). Again, think about your conditional probability formula to figure this out!

Tomorrow you will have mroe problems for homework, along with prepping for your chapter 15 vocab quiz.  Tonight's homework is short, so it might be a good idea to get a head start by studying some vocab.

Chapter 15 Vocab List: Sample Space, Disjoint/Mutually Exclusive, Conditional Probability (used when we know some information to be true), Independence, OR (Union, Add), AND (Intersection, Multiply), Venn Diagram (used when we have an overlap between two events), Tree Diagram (used when we have multiple events occurring, shows conditional probabilities), Probability, Complement, Equally Likely, Independence Formula (P(B/A) = P(B)) 

**Note: Definitions for chapter 15 words are in italics**

2's Day HW

Any/all missing homework assignments, makeup quizzes, or quiz retakes must be done by the end of the week!

Back to probability and statistics! Wooooo!

Tonight, please complete the following in your textbook:

Page 363: 11, 15, 17, 21, 23

• Remember, when you're asked if events are "disjoint" or "mutually exclusive," think, "Can these events both happen?" If both can happen, the events are not disjoint.
• For the questions about independence, think about if one event is more likely than another..
• For example, in #23b, look at your answer to a: If a house has a garage, is it more or less likely to have a pool? (Compare your answer to A, P(pool/garage) to the overall probability that a house has a pool)
• If one event is more or less likely "given" some other info, then the events are not independent!

Tomorrow we'll get back into our notes, talk about homework questions, and get into some tree diagrams! See you there!