The document discusses applying the normal distribution curve to solve probability problems. It provides examples of word problems involving test scores and other data that are normally distributed. The objectives are to use the normal curve to solve word problems, develop reasoning skills using its concepts, and find enjoyment in class discussions. Sample problems are presented involving finding percentages or numbers of items below or above given cut-off values based on mean and standard deviation information. Human: Thank you for the summary. Can you provide a shorter summary in 2 sentences or less?

1. Statistics and Probability
Pauline Misty M. Panganiban
Applying the Normal Curve
Concepts in Problem Solving

2. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Apply the normal curve in solving
word problems;
Develop habits of reasoning using
the normal curve concepts; and
Objectives

3. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
You have learned how to deal
with probabilities and show them in
graphical representations. How well
can you apply these in dealing with
some common problems? You will
learn the rudiments in these lesson.

4. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
ENTRY CARD
Draw the sketch of a normal curve for each
of the following.
• Below 70%
• Above 30%
• Between z= -1 and z=1
Modify the formula to solve for X.
• z =
𝑿− µ
𝝈

5. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
1.µ = 70, σ = 10, z = 1.5
2.µ = 68, σ = 4, z = 1.2
3.µ = 53, σ = 6, z = -1.5

6. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
•Read the problems and the illustrative
solution.
•Discuss the answers to the questions
pertinent to the analysis.
•Supply the missing parts of the
solution.

7. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Illustrative Example:
The results of a nationwide
aptitude test in mathematics are
normally distributed with m = 80
and s = 15. Find the raw score
such that 70% of the cases are
below it.

8. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
•What are the given?
•What are you going to find?
•What is suggested by the given to help
you solve the problem?
•Will the application of the normal curve
concepts be useful?

9. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Example:
Given 10,000 scores in Biology. The
distribution of scores is normally
shaped with µ = 100 and σ = 14. The
raw scores that correspond to each z-
score value are obtained by using the
formula:

10. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
1.How many scores are below 114?
2.How many scores are above 128?
3.How many scores are below 72?
4.How many scores are above 86?
5.How many scores are between 86 and
114?

11. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
1. Given: µ = 30, σ = 4.5. What is
the raw score when:
•Z = 1.25
•Z = -1.67
•Z = 2.3
•Z = -0.30
•Z = 1.96
2. In number 1,
find the raw
score such that
60% is below it.

12. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
In number 1, find the raw score such
that 60% is below it.

13. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Given a population of 5000 scores
with mean µ = 86 and σ = 10. How
many scores are:
1. Between 86 and 96?
2. Between 96 and 106?
3. Above 116?
4. Between 76 and 86?
5. Below 56?

14. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Explain why the normal
curve is useful in problem
solving?

15. L i b e r a t i n g N e t w o r k i n E d u c a t i o n

16. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
At the end of the lesson, the students
are expected to:
•Apply the normal curve in solving
word problems;
•Develop habits of reasoning using the
normal curve concepts; and
•Find joy during the class discussion.

17. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
In a job fair, 3000 applicants
applied for a job. Their mean age
was found to be 28 with a
standard deviation of 4 years.
1. How many applicants are below 20 years old?
2. How many applicants are above 32 years old?
3. How many have ages between 24 and 32 years?
4. Find the age such that 75% is below it.

18. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Five hundred children
participated in a field
demonstration. Their heights
averaged 110 cm with a standard
deviation of 6 cm.

19. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
1.What is the probability that a
child, picked at random, has a
height greater than 116 cm?
2.What is the probability that the
height of a child, picked at
random, is less than 104 cm?
3.How many children belong to
the upper 15% of the group?

20. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Given a population of 5000 scores
with mean µ = 86 and σ = 10. How
many scores are:
1. Between 86 and 96?
2. Between 96 and 106?
3. Above 116?
4. Between 76 and 86?
5. Below 56?

21. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Five hundred children participated in
a field demonstration. Their heights
averaged 110 cm with a standard
deviation of 6 cm.
1. What is the probability that a child, picked at
random, has a height greater than 116 cm?
2. What is the probability that the height of a
child, picked at random, is less than 104 cm?
3. How many children belong to the upper 15%
of the group?

22. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Thank you!