Given a
normal distribution, by the
68-95-99 rule of thumb, about 68
percent of the
data will have a Z-score on the range -1 to 1 inclusive (that is, will be between -1 and 1
standard deviations from the mean), about 95% will have a
Z-score between -2 and 2, and about 99.7% will have a Z-score between -3 and 3. For more accurate values than the 68-95-99 rule, one should consult a
table or
calculator.
A Z-score is often looked up on a
Z-table to determine what
percent of the
data should be within a certain
range, or to find the
probability that an arbitrary
event occurred. On a
TI-83 or
TI-89, the
normcdf and
normpdf (for the former) or
tistat.normcdf and
tistat.normpdf (for the latter) can take the place of a Z-table.
When the
standard deviation of the
population is not known, a
T-score can be used.