STA 2023
Section 5.3
Normal Distributions:
Finding Values
Finding z-scores
 In
the last section, if we had a z-score we can find its
probability.
 In this section we will be given a probability. From
that probability we will be able to work backwards to
find its z-score.
 Example 1: Use the calculator to find the z-score that
corresponds to a cumulative area of 0.3632.




On the Calculator:
Press 2nd, Vars, and choose 3:invNorm(
Syntax: invNorm(area to the left of the z-score)
Answer: invNorm(.3632) = -0.35

Transforming a z-Score to an x-Value


Finding a Specific Data value for a Given
Probability


Example 6: The average time spent sleeping (in hours) for
a group of medical residents at a hospital are normally
distributed with a mean of 6.1 hours and a standard
deviation of 1 hour.

What is the shortest time spent sleeping that would still
place a resident in the top 5% of sleeping times?
 Answer: 7.74 hours.

Between what two values does the middle 50% of the
sleep times lie?
 Answer: Between 5.43 hours and 6.77 hours.