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1. UNDERSTANDING THE NORMAL CURVE
DISTRIBUTION

2. Lesson Objectives
At the end of this lesson, you are expected to:
1. understand the concept of the normal curve
distribution;
2. state and illustrate the properties of a normal
curve distribution;
3. sketch the graph of a normal distribution; and
4. recognize the importance of the normal curve in
statistical inference.

3. Pre-Assessment
Recap: Probability Distributions

4. Lesson Introduction
When scores in a set of data are ordered and their
frequencies are noted, a pattern emerges.

5. Discussion Points
Properties of the Normal Probability
Distribution
 The distribution curve is bell-
shaped.
 The curve is symmetrical about its
center.
 The mean, the median, and the
mode coincide at the center.
 The width of the curve is
determined by the standard
deviation of the distribution.

6. Discussion Points
Properties of the Normal Probability
Distribution
 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.
 The area under the curve is 1. Thus, it
represents the probability or
proportion or the percentage
associated with specific sets of
measurement values.

7. Discussion Points
The Area Under the Normal Curve

8. Discussion Points
The Table of Areas under the Normal Curve is
also known as the z-Table.
The z- score is a measure of relative standing. It
is calculated by subtracting X– (or μ) from the
measurement X and then dividing the result by s
(or σ).
The final result, the z-score, represents the
distance between a given measurement X and
the mean, expressed in standard deviations.

9. Discussion Points
Four-Step Process in Finding the Areas Under the
Normal Curve Given a z-Value
• Step 1. Express the given z-value into a three-digit form.
• Step 2. Using the z-Table,find the first two digits on the left
column.
• Step 3. Match the third digit with the appropriate column on
the right.
• Step 4. Read the area (orprobability) at the intersection of the
row and the column. This is the required area.

10. Example
Find the area that corresponds to z = 1.

11. Example 2
Find the area that corresponds to z = –2.58.
Solution
1. Find the Row z=2.5.
2. Find the Column with the heading 0.08.
3. Read the area at the intersection of Row 2.5 and
Column 0.08.

12. Exercises
Find the corresponding area between z = 0 and
each of the following:
1. z=0.96
2. z=1.74
3. z=2.18
4. z=2.69
5. z=3.00

13. Summary
Properties of the Normal Probability Distribution
 The distribution curve is bell-shaped.
 The curve is symmetrical about its center.
 The mean, the median, and the mode coincide at the center.
 The width of the curve is determined by the standard
deviation of the distribution.
 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.
 The area under the curve is 1. Thus, it represents the
probability or proportion or the percentage associated with
specific sets of measurement values.

14. Summary
Four-Step Process in Finding the Areas Under the Normal
Curve Given a z-Value
Step 1. Express the given z-value into a three-digit form.
Step 2. Using the z-Table,find the first two digits on the left
column.
Step 3. Match the third digit with the appropriate column on
the right.
Step 4. Read the area (orprobability) at the intersection of the
row and the column. This is the required area.