a givens^2 , the curve is bell-shaped with the tails dipping down to the baseline.
In theory, the tails get closer and closer to the baseline but never touch it, pro-
ceeding to infinity in either direction. In practice, we ignore that and work
within practical limits.
The peak of the curve occurs at the meanm(which for this special distribu-
tion is also median and mode), and the height of the curve at the peak depends,
inversely, on the variances^2. Figure 3.3 shows some of these curves.
3.2.2 Areas under the Standard Normal Curve
A variable that has a normal distribution with meanm¼0 and variances^2 ¼ 1
is called thestandard normal variateand is commonly designated by the letter
Z. As with any continuous variable, probability calculations here are always
Figure 3.3 Family of normal curves: (a) two normal distributions with the same mean
but di¤erent variances; (b) two normal distributions with the same variance but di¤erent
means.
NORMAL DISTRIBUTION 123