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AP Statistics 2016-2017
Chapter 8: The Binomial and Geometric Distributions
8.1: The Binomial Distributions
8.2: The Geometric Distributions
"The Great Architect of the Universe now begins to appear as a pure mathematician." -- (James Jeans)
Check out these passages from the Bible: I Kings 7:23 and II Chronicles 4:2. You will find indirect references to indicate that  (pi) is
equal to 3 at each location if you know that the circumference of a circle is given by the formula C = 2( )R. The passages contain these
words and phrases:
Cubit: Originally, this was roughly the distance from one's elbow to the end of middle finger. In English measure, it is about 18 inches.
Molten sea: A high bowl or tank supported on twelve oxen. (Biblical description appears in I Kings 7:24-26.)
Bath: A liquid measure, approximately 6 gallons.
"One cannot escape the feeling that mathematical formula have an independent existence and an intelligence of their own, that they are
wiser than we are, wiser even then their discoverers, and that we get more out of them than was originally put into them."
-- (Heinrich Hertz)
Some 1500 years ago, an American Indian people called the Anasizi lived in what is now the southwestern United States. They, along
with the Navajo and Pueblo tribes, produced coiled baskets, rugs, quilts, and clothing that displayed complex geometric patterns.
Assignment # 1 (Introduction & §8.1) )
M:[12-05-16]
Read pp. 436 – 441 Do Activity 8/A Gaggle of Girls; pp. 442 – 445.
pp. 441 – 442 # 8.1 – 8.2
Assignment # 2 (§8.1)
T:[12-06-16]
pp. 445 – 446 # 8.3 – 8.8
Read pp. 446 – 449; pp. 450 – 454; pp. 455 – 459 Technology Toolbox.
pp. 449 – 450 # 8.9 – 8.14
pp. 454 – 455 # 8.15 – 8.20
Assignment # 3 (§8.1)
pp. 459 – 460 # 8.21 – 8.26
W:[12-07-16]
Assignment # 4 (§8.2)
Th:[12-08-16]
Read pp. 464 – 467; pp. 469 – 473 Technology Toolbox. Take notes on all terminology.
p. 468 # 8.37 – 8.40
pp. 473 – 475 # 8.41 – 8.46
Assignment # 5 (Summary & Review)
F:[12-09-16]
Read pp. 460 – 461; p. 475; pp. 478 – 479. Take notes on all terminology.
pp. 461 – 464 # 8.27 – 8.36
Assignment # 6 (Summary & Review)
pp. 475 – 478 # 8.47 – 8.54
Practice Quizzes and Practice Tests
M:[12-12-16]
Assignment # 7 (Summary & Review)
T:[12-13-16]
pp. 478 – 482 # 8.55 – 8.65
Practice Quizzes and Practice Tests Review
Assignment # 8 (§8.1 – 8.2 Test)
W:[12-14-16]
Key Words, Skills, Terminology and Concepts
Binomial Setting
Binomial Random
Variable
Binomial Probability
Probability Distribution
Cumulative
Function
Distribution Function
Binomial Coefficient
Binomial Probability
Formula
Binomial Mean
Binomial Standard
Deviation
Normal Approximation
to Binomial
Rule of Thumb
Geometric Distribution
Geometric Setting
Geometric Probability
Rule
Geometric
Mean/Expected Value
Geometric Standard
Deviation
P( X > n)
Simulating Binomials
& Geometrics
Usage of the TI-83 – 2nd DISTR 0:binompdf (# observation, p, # successes);
2nd DISTR A:binomcdf (# observation, p, # successes); MATH PRB 3: # nCr #;
MATH PRB 7: randBin(1, p, # of observations) ; MATH PRB 4: #!;
2nd DISTR D:geometpdf (p, # trials);
2nd DISTR E:geometcdf (p, # trials)
"Every new body of discovery is mathematical in form, because there is no other guidance we can have." -- (Charles Darwin)
Persian-born Omar Khayyam (1048-1131) was both a poet and a mathematician. He is the author of a collection of poetry titled
Rubaiyat. He contributed much to mathematics, including finding geometrical solutions for cubic equations and calendar reform,
suggesting a cycle of 33 years that included 8 years with 366 days. Ever the poet, his reforms are referenced in the Rubaiyat:
Ah, but my Computations, People say,
Reduced the Year to better reckoning? Nay,
'Twas only striking from the Calendar
Unborn Tomorrow, and dead Yesterday.
"If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy." -- (Alfred Renyi)
Many of the words we use to describe branches of mathematics are of Greek origin:
Arithmetic: From arithmetike, meaning "the art of counting."
Geometry: From geometrein, meaning "to measure the land."
Mathematics: From the combination of two words; one is manthanein, meaning "to learn." The other is mathema, meaning "science."