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.