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Statistics and Probability
Scan Me!
CURVE
ASYMPTOTE
SYMMETRIC
AREA
BELL-
SHAPED
Do you know your height and weight?
Fig. 1 Distribution of Height of Gr. 11
HUMSS Marx
Fig. 1 Distribution of Weight of Gr. 11
HUMSS Marx
Normal
Distribution
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
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).
Lesson Proper
Normal Probability Distribution
- is a probability distribution of
continuous random variables. It
shows graphical representations of
random variables obtained through
measurement
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.
Properties of Normal Curve
2. The curve is
symmetrical
about its
center.
Properties of Normal Curve
3. The mean,
median, and
mode coincide
at the center
Properties of Normal Curve
4.The width of
the curve is
determined by
the standard
deviation of the
distribution.
Properties of Normal Curve
5. The tails are thus
asymptotic to the
baseline.
Properties of Normal Curve
6. The total area
under a normal
curve is 1.
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.
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
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.
Short
Quiz!
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?

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COT 1 presentation.pptx

  • 7. Do you know your height and weight? Fig. 1 Distribution of Height of Gr. 11 HUMSS Marx Fig. 1 Distribution of Weight of Gr. 11 HUMSS Marx
  • 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.
  • 13. Properties of Normal Curve 2. The curve is symmetrical about its center.
  • 14. Properties of Normal Curve 3. The mean, median, and mode coincide at the center
  • 15. Properties of Normal Curve 4.The width of the curve is determined by the standard deviation of the distribution.
  • 16. Properties of Normal Curve 5. The tails are thus asymptotic to the baseline.
  • 17. Properties of Normal Curve 6. The total area under a normal curve is 1.
  • 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

  1. 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.