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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 possibleat 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 TI82 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 acceptableso I don't worry about either areamuch.



