Math 143 C/E, Spring 2001
IPS Reading Questions
Chapter 4, Section 3
The probability histogram as a mathematical model, arising from the assumptions that the roll you get on one occasion is independent of previous rolls and that all rolls are equally-likely. For dice that satisfy these assumptions, one would expect that a relative-frequency histogram of actual rolls would tend to settle in to the appearance of the probability histogram as the number of rolls n increased. After n=1000 rolls, the actual histogram is libel to look very much like that of the probability model.
It is discrete because scores are always integers. There might be people with scores of 550 and others with 551, but no one gets a score in between these two (or any other pair of) values.
Literally speaking, I was in error. It is the same kind of error we make when we say that the number p is equal to 22/7. The discrete probability distribution for SAT-math scores is very similar in shape to N(500,100) - the latter is roughly what you would see if you blurred your eyes when looking at the former, blurring them enough so as not to see the stair-step effect of the bars at each possible SAT-math score. Moreover, since probabilities are illustrated as areas under these probability-distribution curves, the most important thing is that, for a give value of x, both graphs have approximately the same amount of areas to give values for P(X < x).