This document provides examples of using the standard normal distribution to calculate probabilities from exam scores and efficiency ratings that follow a normal distribution. The first example calculates the probability of a randomly selected student scoring below 45, above 73, below 85, and between 50 and 75 based on exam results with a mean of 60 and standard deviation of 9. The second example similarly calculates the number of faculty with efficiency ratings above 86, above 80, and between 80 and 90 given a mean of 86 and standard deviation of 4.25.

1. APPLICATION of
the STANDARD
NORMAL CURVE

2. Xi – X
z =
s
STANDARD SCORE FORMULA

3. Example #1
The examination results of a large
group of students in Statistics are
approximately normally distributed with
a mean of 60 and a standard deviation
of 9. If a student is chosen at random,
what is the probability that his score is:
a. below 45?
b. above 73?
c. below 85?
d. between 50 and 75?

4. Example # 2:
The efficiency rating of 300 faculty members
of a certain college were taken and resulted
in a mean rating of 86 with a standard
deviation of 4.25. Assuming that the set of
data are approximately normally distributed,
how many of the faculty members have an
efficiency rating of:
a. greater than 86?
b. greater than 80?
c. between 80 and 90?