Search This Blog

Monday, December 29, 2014

Take Home Test Help! and Extra Credit Potential!W

Hope you're all enjoying the break thus far!

I've received a few emails about the take home test already (which is awesome), and a couple things were brought to my attention. Check out the hints/help below:

#10 and #11:
These questions are both binomial probability models. We know they are binomial because we are given a sample size for each. To answer these questions we need to use the formulas for the mean and standard deviation for a binomial probability. The mean of a binomial probability model is = np. In other words, mean = mu = np. The standard deviation of the binomial probability model is found by sqrt(npq). That is, standard deviation = sigma = squareroot(npq). You can also find these formulas in chapter 17.

#12:
There are two ways to do this question. One approach is to use the binomial probability on our calculator (you decide if it's pdf or cdf). If you use this method your answer will not match the multiple choice options (but it is correct); choose the option closest to your answer.

Another approach is to use the Normal model to find a binomial probability. We did not learn this before break. Any time that np > 10 and nq > 10 we can use a Normal model (instead of binomcdf). To find the mean and standard deviation of the Normal model we would have to use the formulas described above (for #10 and #11). Then, we will have a new mean and standard deviation, and we can use these values to calculate a z-score and use normalcdf (like any other Normal model problem). If you use this method your answer will match the multiple choice options.

Both methods are correct.

Keep the questions coming! If I get more questions that I feel will be helpful for everyone, I'll keep posting my responses to emails on the blog!

Extra Credit Opportunity:
Want/need some extra credit?

You can earn 6 points on a quiz grade if you do the following:

  1. Listen to the "Stat Rap" under the "Statistics Music" link on the right.
  2. Write down at least 12 statistics references you hear in the song. You must write the exact lyrics of the song. Number these references.
  3. Then, below each reference, briefly explain what the reference means, statistically speaking. Do not simply define the terms, you must interpret the statistical meaning in the context of the song!
  4. Your explanations must be correct! You will earn 1/2 point for each correct lyric and explanation; if you want to be sure you'll earn all 6 points, feel free to provide extra references!
**This only applies to the "Stat Rap," not the "Stat Rap Remix." (We'll save that one for later...)

Example:
1. "I state the null hypothesis there ain't no way you're stopping this."
  • The null hypothesis is the first thing you state in a hypothesis test, and this is the first line of a song. 
2. "Crossin' all my T's like my name was Billy Gosset."
  • William Gosset developed the t-distribution that is used in Statistics."



Tuesday, December 23, 2014

We Made It!

TAKE HOME TEST IS DUE MONDAY 12/5! You will lose 10 points for each day this is late! You can find a pdf version of the take home test under our classroom resources link (on the right) entitled, "Probability Take Home Test." (It's right at the top).

Other than that, enjoy your break! Rest up, relax, spend time with friends and family, enjoy some gifts, play outside, watch a movie....come back rejuvenated! We'll have plenty of hard work when we get back; we'll learn chapter 11 (feel free to read it if you want a head start) and start 12, and then it's midterm time!

This week is a great time to start studying for your midterm! The best thing you can do is to open up your Barron's book....
  • Use the table of contents to find the topics that we have already learned, and then try the practice problems in the back of these sections! (All of the answers/explanations are also provided)
  • OR, try out a practice test in the back of the book! Your midterm will be a mini AP exam, so doing a  practice test is really the best way you could study; just keep in mind that you will come across questions that you have not learned how to do yet!
Check the blog later in the week...I think I'm going to post an extra-credit opportunity!

Have a wonderful vacation! Thanks for being an awesome AP Stats group! We're halfway to our AP exam!

Monday, December 22, 2014

We're almost there!

One more class!

Tomorrow we will do some more classwork practice with geometric/binomial probability and we'll answer any remaining questions we have!

No (official) homework tonight. However, tomorrow in class I will provide an answer key to some practice problems. It might be a good idea to try them out tonight so you know if you have questions to ask tomorrow! The questions are listed below.

Binomial/Geometric Practice!
According to the 2011 U.S. Census, 20.1% of Americans (aged 5+) speak a language other than English at home.
a. How many Americans would you expect to survey before you find the first person who speaks a language other than English at home?
b. What is the probability that the first person who speaks a language other than English at home is the 50th person surveyed?
c. If you sample 800 Americans aged 5+, what is the probability that exactly 200 speak a language other than English at home?
d. If you sample 800 Americans aged 5+, what are the expected number of people who speak a language other than English at home? With what standard deviation?
e. With a sample of 800 Americans have we met the 10% condition? Explain.
f. What is the probability that the first person who speaks a language other than English at home is surveyed 8th, 9th, or 10th?
g. What is the probability that among 1,000 surveyed Americans (age 5+) exactly 999 speak a language other than English at home?
 
h. What is the probability that in a sample of 5 Americans at least 2 speak a language other than English at home?
 
i. What is the probability that in a sample of 5 Americans at most 4 speak a language other than English at home?
j. What is the probability that in a sample of 1,000 Americans (age 5+) at least 100 speak a language other than English at home?
k. What is the probability that in a sample of 1,000 Americans (age 5+) at most 100 speak a language other than English at home?


Friday, December 19, 2014

It's Friday!

The break is looming....it's sooo close...

Looks like we voted on no vocab test and a take home test on probability. Keep checking the blog for more polls; I liked the democratic decision making process!

Today's update differs by class:

Period B: You have no homework (we did the other classes' homework as our stamp). I am concerned that some of us won't learn what we need to for our take home test. We will have to finish chapter 17 on Monday and Tuesday; however, if you are absent (either because you're just not here or you're at the honors breakfast) you will miss some super important stuff that you need for your take home test. I'm not saying you should skip bingo, but if you're not in class, you're still responsible for what you missed. If you have study hall E or F period I would recommend coming to one of those classes so you're not behind. I have a meeting on Monday and therefore cannot stay after school. I am available during D or H period on Monday, and D,G(lecture hall), and H period on Tuesday.


Periods E and F: Unfortunately, I realized too late (for period B) that I shouldn't have spent so much time on the "Stamp." So, you're homework is to complete the "Stamp" problem provided in class (or found below). This is some probability review! On Monday and Tuesday we'll finish learning about binomial probability so we can ace our take home test!

Have a great weekend!


"Stamp Problem" Homework:

The article "Checks Halt over 200,000 Gun Sales" (San Luis Obispo Tribune) reported that required background checks sometimes block gun sales. The article indicated that state and local police reject a higher percentage of would-be gun buyers than does the FBI, stating, "The FBI performed 4.5 million of the 8.6 million checks, compared with 4.1 million by state and local agencies. The rejection rate among state and local agencies was 3%, compared with 1.8% for the FBI.
a.) What is the probability that a randomly selected gun sale was checked by the FBI and was not rejected?
b.) What is the probability that a sale that was rejected was checked by the FBI?
c.) What is the probability that a randomly selected gun sale was rejected?
d.) What is the probability that a sale that was checked by the FBI was rejected?

Thursday, December 18, 2014

Vote on the Polls!

Back to the grind...one more chapter of probability...

Tonight, please complete the following in your textbook:

Page 398: 1,7,9,11

Tomorrow in class we'll start to talk about some binomial probability! See you there!


Period B: I think I may have changed my mind...I'm afraid that if we have a vocab test on Monday we will not be able to finish chapter 17 before break...so I'm leaving it up to you...

Everyone: vote on the poll on the top right if you want to have a say in whether we have a test or not on Monday! This decision will be made entirely based on the poll results!

Also, vote if you'd like to have a say in whether we have a take home or in class test for our probability unit!

Wednesday, December 17, 2014

Wed nes day HW

Everyone got an A on today's quiz....right?

Tonight, please complete the chapter 17 reading questions (provided in class, or listed below):
You can find all of these answers in chapter 17 of your textbook!

1.       What are the three qualifications for a situation to be a Bernoulli trial?
2.       What is a Geometric probability model used to calculate?
3.       What is the 10% condition?
4.       A Binomial model is defined by two parameters. What are these?
5.       The formula for a binomial probability is highlighted (middle of the page) on page 391. What is this formula?
6.       What do each of these variables—n, k, p, and q—represent? 
7.       Look on page 391, just above the box at the bottom, the (blue) highlighted sentence. Write this sentence. (“A binomial probability model describes…)
8.       What are the formulas for mean and standard deviation of a Binomial probability model (look at the box on page 391).
9.       What is the success/failure condition? It is used to determine if we can use….(what)
10.   Look at the TI Tips box on page 393. What is the difference between binompdf( and binomcdf( ?

Tomorrow in class we'll get into our chapter 17 notes...we'll take notes for Thurs/Fri/Mon/Tues to finish our unit on probability...exciting stuff!

Tuesday, December 16, 2014

Quiz Tomorrow!

Tomorrow we will have our chapter 16 quiz. Your homework tonight is to study!

The quiz is broken into two parts: vocab and "math problems."
  • Chapter 16 Vocab:
    • Probability Model
    • Expected Value
    • Variance
    • Standard Deviation
    • Random Variable
    • Discrete Random Variable
    • Continuous Random Variable
    • Shifting
    • Rescaling
    • Pythagorean Theorem of Statistics (variances always add!)
    • Decide which scenario does not require conditional probability
    • Disjoint/Mutually Exclusive
    • Complement (of an event, A)
  • Chapter 16 "Math":
    • Pretty much just study the chapter 16 outline (typed) I provided you in class!
    • Find the expected value and standard deviation given a probability model
    • Interpret expected value (in context, in a sentence)
    • Use the Normal model to find probabilities
    • Find the mean and standard deviation for a sum or difference of random variables
      • Use this mean and standard deviation with a Normal model
      • Study #33 from your hw! And the AP problems from class Monday!

Monday, December 15, 2014

Monday HW!

Only one more Monday before our break...

Until then, hard work.

Tonight, please complete the following in your textbook:

Page 381-384: 27, 33, 37

Tomorrow in class we'll answer homework questions and talk about our chapter 16 quiz on Wednesday. Then, it's on to chapter 17! See you there! Enjoy your sunny afternoon!

Friday, December 12, 2014

Weekend HW!

This weekend, please complete the two AP problems provided in class (only one looks like an AP Problem). If you lost yours or you were absent, you can find them below. (We did not learn anything in class on Friday that is required to complete this homework!)

Here are some homework hints if you're stuck:
  • For the first question ("Uncovering Expected Value"), remember that the probabilities given represent playing this game one time. The probability model that you have to complete is for the sum of the scores from your games if you play twice.
    • To complete the probability model, you must first consider how you could get a sum of 0,1,2,3, or 4. Then, use this idea to find the probability.
    • For example, to get a sum of 0, we would have to get "0 first and 0 second." This probability would be "0.4 x 0.4," which is .16. Use the same type of idea to complete the table. If you're stuck, think first in words, then numbers (just like when we started probability!
  • For the second question, part (a) should be fairly straight forward. Part (c) deals with the median of a probability distribution; this is not something we would learn in class. It is your job to use the definition of median (provided in the question) to try to answer this question.
    • Part (d) then brings back some of the ideas from the start of the year that address how the mean and median compare for different shapes of a distribution.
    • And you can find the scoring rubric here: 2005 #2 Scoring Rubric
      • And even though you skipped it, check out the answer to (b)!


 
Enjoy the weekend! One more full week before break! Woooooo!
 
 

Thursday, December 11, 2014

Thursday Homework

The Normal model is back!

We'll be working with the Normal model (in addition to the stuff we've been learning) for the next few days...the more fluent you are in working with it, the easier this stuff will be! Check your chapter 6 notes, chapter 6 in your book, or the Normal model section of you Barron's book to review!

Tonight, please complete the worksheet provided in class. You can find the questions below if you lost yours.
  • To find the probabilities for this probability model, you will need to find some z scores and either use a z-table or normalcdf!*
  • For #1, the answer are: a.) 0.0475; b.) 0.7493; c.) 0.1971; d.) 0.0062
  • I didn't teach you how to do 7 yet! Try your best! Take a guess!

Also, I am going to grade this as a homework, not a 16 point classwork...just do your best! I'll provide an answer key tomorrow!

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 65 points: $0

b.      From 65 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. 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)

  1. If the teacher plans to quintuple each prize (multiply by 5), find the new expected value and variance. (2 points)
  2. 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, December 10, 2014

Wednesday HW

Tonight, please complete the following in your textbook:

Page 381: 3/11, 5/13, 7, 15
**This says 3/11 and 5/13 because #11 asks for the variance from number 3...so it is probably easier to do these two questions together (and #13 asks for the variance from 5)**

**Remember, to find the variance use your graphing calculator! Check out page 372 for calculator help!**

Tomorrow in class we will answer any homework questions, then we'll start to move on and discuss how expected value and variance will (or will not) change when we "shift" or "rescale" our outcomes! (Sound familiar?)

Then, we'll bring back the Normal model and start to discuss how we combine random variables. See you there!

Have a great afternoon!

Tuesday, December 9, 2014

No Stat Homework?!

No homework? What?

Tonight, just enjoy the rain. Or, enjoy some sweatpants, a blanket, and some Christmas movies.

Oh yeah....and study whatever you didn't know how to do on today's quiz! Tomorrow you will have 10-15 minutes to finish!

Monday, December 8, 2014

Quiz Review Questions!

A second update today?! That's right!

Today we had about 10-15 people in the room working on some review questions for tomorrow's quiz....which was AWESOME. I would love to see this happen more often to study for a quiz/test!

Check the blog post below for an outline of the test...

If you're looking to study, here are the review questions we worked on after school to study for the quiz! The answers are in parentheses...if you can do all these, you're in great shape for tomorrow!


Probability Review Questions (for ch. 14/15 quiz)

1.)    A player spins a spinner. 40% of the spinner is green, 20% is red, 15% is blue, 15% is yellow, and the rest is orange.

a.       What is the probability that the spinner lands on orange? (0.10)

b.      What is the probability that the spinner lands on green or red? (0.60)

Suppose we spin the spinner 5 times….

c.       What is the probability that all 5 spins land on red? (0.00032)

d.      What is the probability that none of the 5 spins lands on red? (0.32768)

e.      What is the probability that the first red is the fifth spin? (0.08192)

f.        What is the probability that at least one spin is red?  (0.67232)

g.       What is the probability that exactly one spin is red? (0.4096)

h.      What is the probability that the spins land in this exact order: red, green, red, green, orange (0.00064)

2.)    Suppose that the probability someone has a given disease is 0.12. A person will take a test to see if they do in fact have this disease. 95% of people who have the disease will test positive, and 92% of people who do not have the disease will test negative.

a.       What is the probability that someone has the disease and tests negative? (0.006)

b.      What is the probability that someone has the disease and tests positive? (0.114)

c.       What is the probability that someone who has the disease tests positive? (0.95)

d.      What is the probability that someone who does not have the disease tests positive? (0.08)

e.      What is the probability that someone has the disease, given they tested positive? (0.6182)

f.        What is the probability that someone has the disease if we know they tested negative? (0.0074)

3.)    Suppose that 80% of students take math in their senior year, 65% of students take science their senior year, and 55% take both.

a.       What is the probability that a student takes only science? (0.10)

b.      What is the probability that a student takes math or science, but not both? (0.35)

c.       What is the probability that a student takes neither course? (0.10)

d.      What is the probability that a student who takes science takes math? (0.8461)

e.      What is the probability that a student who takes math takes science? (0.6875)

4.)    There are 20 marbles in a bag. 8 are blue, 6 are red, 4 are green, and 2 are black. You plan to create a “collection” of 4 marbles.

a.       What is the probability that all 4 marbles are blue? (0.01444)

b.      What is the probability that your collection does not have any black marbles? (0.6316)

c.       What is the probability that all of the marbles in your collection are the same color? (0.01776 to 0.0195; depends on how you round)

STUDY!

Tomorrow we have a big quiz....chapters 14 and 15....this is a nice opportunity to see where we stand at the halfway point of the probability unit. Study hard and get an A!

Here's a breakdown of the topics that appear on tomorrow's quiz:
  • Finding probabilities using "AND" and "OR" (study you chapter 14 quiz)
  • "At least one" and "exactly one" problems (look at our chapter 14 quiz, or stamp from Friday, and/or #1 and #6 on the 13 question multiple choice quiz we had)
  • Venn diagram questions (study the worksheet we did in groups with 4 different Venn diagram contexts)
  • Probabilities with tree diagrams (like the worksheet with the drinking/college graduation rates or the homework we did Weds/Thurs)
  • Conditional Probability
    • with tree diagrams
    • with Venn diagrams
    • with contingency (two-way) tables (like the boys/girls/sports/popular/grades example in our notes, or like the back page of your take home test)
    • in other contexts (without any of the diagrams above)
  • Probabilities without replacement
    • Like the "batteries" homework question (ch. 15 #19, I think) (or, study the stamp problem we had where we were making a 4 person committee)
  • STUDY your old quiz, your take home test, and your notes and homework!
Period F: You also have tonight to complete the tree diagram classwork if you would like to add any points to your grade; these are due no later than tomorrow!

Friday, December 5, 2014

Yay for the Weekend!

We made it through another week (already)....this year just seems to be flying by...

This weekend, please complete the 2 AP problems provided in class. You MUST grade your 2011 AP problem to receive credit! (Use the link below). Also, you can find the AP problems below if you lost yours or you were absent.
  • The 2011 question is one of the tougher AP problems I've seen...do your best! Welcome the challenge and figure it out! If you're totally stumped, read through the answer and the rubric to gain an understanding of the question and work backwards!
  • The 2004 question is modified, so you can only use the rubric to grade part A. Use the answers provided for b,c, and d to grade your answers...your job is to show all of the work. This is great review for our midterm!
  • Here are the scoring rubrics:


Thursday, December 4, 2014

Thursday HW....

Tonight, please complete the following in your textbook (if you haven't already):

Page 366: 35 - 45 (odd)

*Remember, the worksheet I gave you in class is these same problems from the textbook, just typed up...so if you lost it, use your book! And check your answers in the book!*

Also, we will have a major quiz on Tuesday. Tomorrow in class we will do some more practice (or STAR), and then we will move onto chapter 16 on Monday. I will be after school on Monday to review for the quiz; the quiz will cover everything that we have learned about probability thus far!

Wednesday, December 3, 2014

Vocab Quiz Tomorrow!

Tomorrow we will have our chapter 15 vocab quiz. The list is below:
  1. Sample Space
  2. Mutually Exclusive
  3. Independence
  4. Probability
  5. Complement
  6. Equally Likely
  7. Venn Diagram
  8. Tree Diagram
  9. Conditional Probability: When do we use it?
  10. Conditional Probability Formula
  11. Independence Formula
  12. Determine if events are independent, disjoint, or neither
Also, please complete the following in your textbook. These problems will be checked on Friday:

Page 366: 35-45 (odd)

*The handout I gave you in class is the same problems from your book, just typed on separate paper*

Enjoy! See you all tomorrow!

Tuesday, December 2, 2014

Tuesday HW

Good work today! Tomorrow we'll continue to work with some conditional probability...we'll look at the insurance example (on the back of the paper we started today) and then you'll have some practice on your own!

Tonight, please complete questions a-g on the worksheet we started in class. Here is the worksheet (in case you were out or lost yours):

Homework Questions:
Example 2: HIV Testing

The OraQuick In-Home HIV Test: Oral fluid HIV tests are very accurate. In studies, the OraQuick oral fluid test detected 91.7 percent of people who were infected with HIV, and 99.9 percent of people who were not infected with HIV.
The prevalence of HIV is estimated to be about 0.5% in the general population.Oral fluid HIV tests are very accurate. In studies, the OraQuick oral fluid test detected 91.7 percent of people who were infected with HIV, and 99.9 percent of people who were not infected with HIV.If you have more questions about oral fluid HIV tests, talk to your doctor or healthcare provider. He or she can help you figure out the best test for you.Oral fluid HIV tests are very accurate. In studies, the OraQuick oral fluid test detected 91.7 percent of people who were infected with HIV, and 99.9 percent of people who were not infected with HIV.

If you have more questions about oral fluid HIV tests, talk to your doctor or healthcare provider. He or she can help you figure out the best testa.)   Create a tree-diagram to model the scenario above.
b.)   What is the probability that an individual has HIV and tests negative?
c.)   What is the probability that an individual does not have HIV and tests positive?
d.)   What percent of people who take the OraQuick test will test positive for HIV?
e.)   What is the probability that someone has HIV if we know they tested positive using the Oraquick test?
f.)    What is the probability that someone who tested positive with the Oraquick test actually does not have HIV?
g.)   What is the probability that someone who tested negative actually does have HIV?

Monday, December 1, 2014

Monday HW!

Back to work...

Tonight, please complete the following in your textbook...

Page 362-366: 9, 11, 15, 21

Tomorrow in class we will continue to explore conditional probability and tree diagrams with some classwork examples. Here's the tentative plan for the week...

Tuesday: Ch. 15 Notes: Conditional and Tree Diagrams
Wednesday: Ch. 15 Notes/Practice
Thursday: Ch. 15 Vocab Quiz, more chapter 15 practice
Friday: Ch. 15 Quiz (or STAR testing...)

See you all tomorrow for some more hard work!