MATH 170 - Applied Statistics
Section 7.6 Normal Distribution – Part II
1Z-Scores and the Normal Distribution
Previously we talked about calculating:
•Probabilities of standard normal random variables using:
–z-tables, or
–TI-83
•Probabilities of normally distributed random variables with mean µand standard deviation
σusing:
–TI-83 ... Only!!!
Now we’ll discuss how to evaluate normally distributed random variables with mean µand stan-
dard deviation σusing the z-tables. The key is:
Convert from
a probability in terms of the original variable (P(a≤x≤b))
to
a probability in terms of it’s z-scores (P(c≤z≤d))
How do we figure out what the cand dare in P(a≤x≤b) = P(c≤z≤d)? First we must recall the
formula for calculating a z-score:
The z-score associated with the value a, where the random variable is normally distributed with mean
µand standard deviation σis the number of standard deviations ais away from the mean
and is computed by
z=
