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Topic: Binomial probabilities
Replies: 0

 Rudy Wiegand Posts: 18 Registered: 12/6/04
Binomial probabilities
Posted: Feb 6, 1997 10:11 AM

I address two areas: 1) the ethics of calculator "implanted" information on
the AP exam and (2) binomial distribution approximated with Normal.

1) In my class, I discuss the ethical approach to appropriate calculator
"programs" only in passing. Most, if not all, of my students would NOT do
so unless continually reminded that it is possible--at which point they
would convince themselves that "everyone else is doing it and they will do
better because of it."

2) As I indicated a couple of weeks ago, I gave my students a binomial
program for the TI-82 which would handle up to n = 354. This allowed us to
discuss the shape of the distribution for small/large p and thus the
efficacy of the normal approximation under that situation. It wouldn't take
much to make the program work for ANY n, using logarithms. Hence, the
normal approximation to the binomial is really passe'. We are way behind,
my fault, a reasonable schedule and just now doing hypothesis testing on mu,
with p to follow. At that point I'll discuss the critical Z value AND THEN
discuss the critical X value(s) using the actual Ho BINOMIAL distribution.
My concern, implicitly asked by several of us, is "will the board make
certain the student knows the intent is to use the approximation OR at
least, at a minimum, ensure that multiple choice answers are NOT so close to
the true binomial value that a distractor is perceived as the BEST answer?"
I believe the Board has chosen problems in which the approximated values and
true values are close enough to provide the same multiple choice answer and
that the free response portion will be graded in a manner that would make
EITHER way acceptable--so I don't worry about either area-----much.