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Pr(Z<...) How much by hand.
Posted:
Nov 3, 1996 8:14 PM


The TI83 allows us all to calculate (and if we want) see the shaded region under various normal curves. Modern learning theory suggests that students are more likely to get the correct answer by first using the TI to do problems rather than having their attention divided between going to tables and manipulating partial areas and, at the same time, trying to understand conceptual what is going on. In other words, technology allows us to learn the concepts first and then particulars later.  Having said that I find that I am having my students do both the following simulatenously:
a) complete write ups by hand using tables and probability notation Pr(z < ....) with no calculators,
and
b) checking their work using the full features of the TI.
While I am only a few days into this, my students say they find it very satisfying to do it by hand and then check it by calculator...the calculator confirmation makes them feel as if they really understand it (since they generated an equivalent solution rather than just getting it out of an answer key.)

Questions:
1) If you are doing both tables and nontable (calculator only) work what order do you do it in?
2) Do we really need tables anymore? Remember we certainly do not need or use trig tables anymore yet when scientific calculators first came out many argued that trig tables were essential. Are there some types of statistics questions which can only be approached if you understand table look up????
3) Let's assume that we only use the calculator  no tables. Since the calculator can calculate the area between two values for any normal curve
[e.g. normalcdf(40,82, 50,10) returns the area between 40 and 82 for N(52,10))]
should we be dealing with symmetry type questions? For example, should they know that they could do the previous example as
normalcdf(10000000,82, 50,10)  normalcdf(10000000,40, 50,10)?
I feel that they should be I cannot explain why.
Albert Coons Mathematics Department Buckingham Browne & Nichols School Cambridge, MA 02138 (617) 5476100 x 264 AlCoons@aol.com



