The document presents an overview of the normal distribution, defining it as a continuous frequency distribution with a bell-shaped curve where the mean, median, and mode are equal. It emphasizes its importance in making inferences about variables assumed to be normally distributed, as well as discussing the empirical rule and its mathematical representations. An example is provided to illustrate the application of the normal distribution in interpreting exam scores.

1. NORMAL
DISTRIBUTION
Presented By : Group 2
Alexa Carcha & Angelo Villanueva

2. DEFINITION
• It is defined as a continuous frequency
distribution of infinite range.
• The normal distribution is a descriptive
model that describes real world
situations.

3. IMPORTANCE
• Many dependent variables are commonly
assumed to be normally distributed in
the population
• If a variable is approximately normally
distributed we can make inferences
about values of that variable

4. • Bell-Shaped
CHARACTERISTICS

5. • Mean=Median=Mode
CHARACTERISTICS

6. • Curve is
asymptotic to
the x-axis
• Total area under
the curve above the
x-axis = 1 or 100%

7. EMPIRICAL RULE:

8. THE NORMAL DISTRIBUTION:
as mathematical function (pdf)
Mathematical Formula

9. THE STANDARD NORMAL
Distribution (Z)

10. 6

11. PROBABILITIES ARE DEPICTED BY AREAS
UNDER THE CURVE
• Total area under
the curve is 1
• The area in red is
equal to p(z > 1)
• The area in blue is
equal to p(-1< z <0)

13. EXAMPLE
Scores on an exam are normally distributed with a
mean of 65 and a standard deviation of 9.
Find the percent of the scores.
a) less than 54
b) at least 80
c) between 70 and 86
10

14. Presented By : Alexa Carcha
Normal Distribution
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