While all normal curves are symmetric, bell-shaped, and follow the 68-95-99.7 rule, non-normal curves can have these two aspects as well. But, if a curve comes from a formula like the one on p. 71, then it (definitely) is normal.
Three reasons are given on p. 71. First, they often provide good descriptions for real data. They “are good approximations to the results of many kinds of chance outcomes.” Finally, many statistical inference procedures (procedures which provide answers to specific questions along with a statement of how confident we can be about our conclusions) are “based upon normal distributions and work well for other roughly symmetric distributions.”
To determine the number of aktars, you would subtract
B's height from A's and divide by 16.5. The idea
is basically the same as the standardized score.
If x is a value that lies along the horizontal
axis under a normal curve N(m, s), then
the standardized score (or z-score) of x tells
how many s's x is larger than m.
Conversion to a z-score has one main purpose. If X is a normally distributed variable, the question of what percentage of X values lies below a certian (fixed) X-value x (or, in symbols, “X < x”), is easily answered using the table of Standard Normal Probabilities (Table A) once we have the z-score that corresponds to the value x.
First, you must envision the standard normal distribution N(0,1) (so Z=0 is the center of the distribution and s = 1 is the s.d.). From Table A, a z-score such as z=1.55 (which can be located along the horizontal axis under N(0,1)) corresponds to the value 0.9394. This means roughly 94/ standard normal curve lies to the left of the value 1.55. (Similar correspondences from Table A can be visualized as percents of the overall area under N(0,1) up to the particular z-score.)