9. Learning Objectives:
› the students are expected to:
a. define normal random variable
b. illustrate normal random variable and
its characteristics
c. state and apply the concepts of the
empirical rule or 68%-95% - 99.7% of
the distribution
10. Construct Me!
The distribution of the
height (X) in
centimeter (cm) of the
16 teachers of LNHS
was presented below.
Construct a histogram
for the random
variable (X).
11. Lesson Proper
Normal Probability Distribution
- is a probability distribution of
continuous random variables. It
shows graphical representations of
random variables obtained through
measurement
12. Properties of Normal Curve
1. The normal
curve is bell-
shaped.
The graphical representation of the normal distribution is popularly
known as a normal curve.
18. EMPIRICAL RULE
1. About 68% of the area under
the curve falls within 1 standard
deviation of the mean.
2. About 95% of the area under
the curve falls within 2 standard
deviations of the mean.
3. Nearly the entire distribution
(About 99.7% of the area under
the curve) falls within 3 standard
deviations of the mean.
19. Group Activity SKETCH ME!
1. bell-shaped
2. Symmetrical
3. asymptotic
Directions: Sketch the following properties or characteristics then
label it.
4. mean, median and mode
are equal
5. standard deviation
6. the total area under
normal curve is 1
20. Let’s Sum It Up COMPLETE
ME!
1. The total area of the normal curve is ________.
2. Normal probability distribution is used to determine
the probabilities of a _________ random variable.
3. The mean, median and mode in a normal
distribution have __________value.
4. The width of the curve is determined by the
__________ of the distribution.
5 The normal probability distribution has a mean μ =
___ and standard deviation ơ = ______.
Directions: Fill in the blanks with the correct statement.
22. ADDITIONAL
ACTIVITY (GIVE
ME MORE!)
The distribution of the
grades of the Senior
High School students in
Statistics and Probability
for the Third Quarter is
shown.
Using the empirical rule,
what can you say about
the distribution of the
grades of the Senior
High School in Statistics
and Probability?
Editor's Notes
You can easily understand the functions of normal probability distribution in our real-life world using the empirical rule. Because this rule is used to roughly test the distribution’s normality, if many data of a random variable fall outside the lower and upper limits of the three-standard deviation, this means that the distribution is not normal.
