"Pure chance is now considered to lie at the very heart of nature, and one of the greatest triumphs of human intellect during the last century has been the discovery of how the operation of chance, synonymous as it is with chaos and randomness, leads to so much structure, order, and regularity in the Universe." -- (Brian S. Everitt, London, August 1999) Sofia Kovalevskaya (Russia, 1850-1891): Despite many prejudices against women, Kovalevskaya was able to receive a good education because of the wealth of her family. She became one of the nineteenth century's most important mathematicians in addition to making significant contributions in the fields of science, poetry, and literature. She wrote novels about the hardships of life in Russia and worked to improve educational opportunities for women. Among many other things, she discovered that the rings of Saturn are egg-shaped ovals (not ellipses). What does Herkimer call writer's cramp? Answer: Author-itus. Things Herky would like to know: Are Venetian blinds made by shady characters? How come you can catch a cold, but you can't catch a warm? ASSIGNMENT #47 Reading: YMM text, Section 8.1, pages 414- 427. Cartoon Guide to Statistics, pages 75-78 (to bottom of page). Section 8.1 Summary (Link to Section Summaries). Exercises: None (just take time to understand the reading).

You are in Section 8.1.

The binomial probability formula (YMM page 426,Cartoon Guidepage 76) uses the notation ( nr )for nCr ,which is on yourcalculator. Note also that under DISTR on your calculator, you haveoptions 1,2, and 3 which we have used before. If you scroll down, youwill find binompdf( and binomialcdf( . We will make great use of these.

The binomial setting is described on page 416. Ilike to simply the explanation a bit and think in terms of slots. Ina binomial setting, you have a specified number of slots with thesame probability of filling each slot. For instance, if I roll a diefive times, we can ask "What is the probability that I will getexactly two 6's?" Note that each roll isindependent of any other roll. OK, thinkof five slots:

___ ___ ___ ___ ___

The probability that I fill any slot with a 6 is1/6. I want to fill exactly two of the slots. The probability that Ifill exactly two of the five slots with a 6 is

Using the TI-83, binompdf(5,1/6,2) = .1607510288.With binompdf( ,you "feed it" the number of slots, the probability of filling a slot,and the number of slots you want filled.

Since we are on a roll (pun intended), we willjust note here that binomcdf(5,1/6,2) = 0.964506.What is this? OK, this is the probability that in five rolls of adie, you would get at most two 6's. This is binompdf(5,1/6,2) +binompdf(5,1/6,1) + binompdf(5,1/6,0) = .160751 +.4018775 + .4018775. (Check it out!)

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Text:
The Practice of Statistics, by Yates, Moore, McCabe. New York,W.H. Freeman and Company, 1999. (ISBN 0-7167-3370-6)

Supplemental books:
The Cartoon Guide to Statistics, by Gonick and Smith. NewYork, HarperCollins Publishers, 1993. (ISBN 0-06-273102-5)
How to Lie with Statistics, by Darrell Huff. New York, W.W.Norton & Company, 1982 (ISBN 0-393-09426-X)