This document discusses the normal distribution and its key properties. It defines the normal distribution as a continuous probability distribution with a bell-shaped graph. The normal distribution is symmetrical, and its mean, median and mode all coincide at its center. The width of the distribution is determined by the standard deviation. It then outlines the empirical rule for normal distributions and introduces the standard normal distribution, where the mean is 0 and standard deviation is 1.

1. TOPIC 2: NORMAL
DISTRIBUTION
BY: JESSA R. ALBIT

2. LESSON 1: UNDERSTANDING THE NORMAL
CURVE DISTRIBUTION
Objectives:
At the end of this lesson, you are expected to:
• Understand the concept of the normal curve distributions;
• State and illustrate the properties of a normal curve
distribution;
• Sketch the graph of a normal distribution; and
• Recognize the importance of the normal curve in statistical
inference.

3. THE NORMAL DISTRIBUTION
• A probability distribution for a continuous random variable X
where its graph is a normal curve.
• also known as the bell curve or the Gaussian distribution
• Carl Friedrich Gauss derived the equation of probability density
function.

4. PROPERTIES OF THE NORMAL PROBABILITY
DISTRIBUTION
1. The distribution curve is bell-shaped.
2. The curve is symmetrical about its center.
3. The mean, the median, and the mode coincide at the center.
4. The width of the curve is determined by the standard deviation of the
distribution.
5. The tails of the curve flatten out indefinitely along the horizontal axis,
always approaching the axis but never touching it. That is, the curve
is asymptotic to the base line.
6. The area under the curve is 1. thus, it represents the probability or

5. N
O
R
M
A
L
C
U
R
V
E

6. EMPIRICAL RULE FOR ALL BELL-SHAPED
DISTRIBUTION
•Approximately 68% will lie between the mean and 1
standard deviation above and below or within the
interval (𝜇 + 𝜎, 𝜇 − 𝜎).
•Approximately 47.5% will lie between the mean and
2 standard deviation above and below or within the
interval (𝜇 + 𝜎, 𝜇 − 𝜎).
•Approximately 49.75% will lie between the mean and
3 standard deviation above and below or within the

7. STANDARD NORMAL DISTRIBUTION
A special case of normal
distribution where the mean is
equal to 0 and the variance and
standard deviation is equal to 1.
Its curve is called standard
normal curve.
A continuous random variable
having a standard normal
distribution..
It is denoted by Z. its value is
called the z-score.

8. STANDAR
D
NORMAL
CURVE

9. AREAS UNDER THE NORMAL CURVE

10. FINDING THE AREA TO THE LEFT OF A
SPECIFIED Z-SCORE
1. Determine the area to the left given that z=2.24. draw the
curve and shade the area under z.