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"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.
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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?
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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.
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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
LINK TO STATISTICS HOME
PAGE
=======================================
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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