"As the sun eclipses the stars by its brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them." -- (Brahmagupta) Brahmagupta (c. 598 A.D.): One of the greatest of Indian mathematicians, Brahmagupta was instrumental in the development of algebra for problem solving. Among other things, he wrote an amazing mathematical treatise in which he covered subjects such as square and cube roots, and fractions. He also enjoyed working with irrational numbers, such as the square root of 2, and calculated values of irrational numbers accurate to many decimal places. What did Herkimer say when he saw a boy and his father being treated to dinner by a hockey goalie? Answer: "I've seen the father, son, and the goalie host." Things Herky would like to know: When a mathematician hits a drive on a golf course, is it OK if he loudly yells "square root of 16"? Would it be necessary for the president of a janitor's union to call for sweeping reforms? ASSIGNMENT #49 Reading: Review Section 8.1, as necessary. Read Summary, page 432-433. Exercises: 8.19, 8.20, 8.21, 8.22, 8.23. You can write neatly in book. Make sure you understand what you are doing. Don't be mechanical at this stage of the game. Your results should make sense to you.

You are in Section 8.1.

Outline for a binomial setting:

• Herky Airlines planes have 50 seats.
• 90% of ticket purchasers show up for flights.
• President Herkimer decides to sell 55 seats for each flight.
• Let x = the number of ticket purchasers who show up.
• x is a random variable with 56 possible values: x is a member of the set {0,1,2,3, ...,54,55,56}.
• This is a binomial setting with N = 55 and p = .9
• mx = 55(.9) = 49.5
• sx = sqrt[55(.9)(.1)] = 2.2249

You can do a nice analysis of this on your TI-83. Put the number 0,1,2,...,54,55 in list L1. This can be easily done by putting cursor on the L1 at the top of the list column and then entering seq(x,x,0,55,1). ENTER inserts the desired numbers in L1.

You can put the corresponding probability values in list L2 by putting the cursor on L2 at the top of the list column and then entering binompdf(55,.9,L1). ENTER inserts the probabilities in L2.

You can get a probability distribution shown on the graphics screen. Turn Plot1 on, choose histogram, make L1 your Xlist, and L2 your Freq. If in WINDOW, you set Xmin = 30, Xmax = 60, Xscl = 1, Ymin = -.1, Ymax = .3, Yscl = 1, Xres = 1, and then GRAPH, you should see a probability distribution histogram on the screen. You can fiddle with the WINDOW, but you must remember that for histograms, (Xmax - Xmin)/Xscl must be 47 or less. Otherwise you will get an error statement.

LINK TO SECTION SUMMARIES

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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. New York, 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)

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