Lesson Plan: Identifies regions under the normal curve corresponding to different standard normal values.

 

DAILY LESSON LOG in Statistics and Probability (3rd Quarter)

Table of Content (toc)

I. Objectives:

LC: Identifies regions under the normal curve corresponding to different

standard normal values.

At the end of the lesson, the learners should be able to:

• Identifies regions under the normal curve corresponding to different
  standard normal values.

II. Content: Identifying regions under the normal curve corresponding to different

standard normal values.

III. Learning Resources:

IV. Procedures:

A. Reviewing previous lesson or presenting the new lesson:

• The teacher will briefly review the previous lesson on the normal distribution and introduce the new lesson on identifying regions under the normal curve.

B. Establishing a purpose for the lesson:

• Provide examples and instances of the content and competencies to clarify concepts and solidify learning.

C. Presenting illustrative examples/instances of the lesson:

• The teacher will present examples of normal distributions and how to identify the regions under the curve.

D. Discussing new concepts and practicing new skills #1:

• The teacher will guide the students in pairs or groups to discuss the new concepts and practice identifying the regions under the normal curve. The teacher will also provide feedback and assess their progress.

ACTIVITY

• The teacher will guide the students in pairs or groups to discuss the new concepts and practice identifying the regions under the normal curve. The teacher will also provide feedback and assess their progress.

Objective: To develop mastery in identifying regions under the normal curve corresponding to different standard normal values.

Materials:

• Graph paper
• Pencil
• Standard normal distribution table (optional)
• Instructions:

• Distribute graph paper and pencils to the students.
• Ask them to draw the x-axis and y-axis on the graph paper, labeling them appropriately.
• Next, ask the students to plot the standard normal distribution curve on the graph paper using the following steps:

    a. The mean is at the center of the x-axis, which is labeled as 0.

    b. The standard deviation is represented by the width of the curve.

    c. The area under the curve represents the probability.

    After plotting the curve, ask the students to identify the regions under the curve     corresponding to different standard normal values. For example:

    a. The region to the left of -1 standard deviation represents approximately 34.13%     of the data.

    b. The region between -1 and 1 standard deviation represents approximately 68.26%     of the data.

    c. The region to the right of 1 standard deviation represents approximately 34.13%     of the data.

    d. The region to the left of -2 standard deviations represents approximately 2.28%     of the data.

    e. The region between -2 and 2 standard deviations represents approximately     95.44% of the data.

    f. The region to the right of 2 standard deviations represents approximately 2.28% of the data.

• Students can also use a standard normal distribution table to check their answers and compare their work with the table.
• Encourage students to label and color-code their graphs to enhance their understanding and retention of the concept.

E. Discussing new concepts and new skills #2:

• Students will present their output in front of the class.

F. Developing mastery (guides formative assessment):

• Ask students to create their own real-life scenarios where normal distribution can be observed (e.g., heights of people, test scores, etc.).
• Students can work in pairs or groups to compare and discuss their graphs and findings.
• For advanced students, ask them to solve problems involving the normal distribution, such as finding probabilities or z-scores for given data.

G. Making generalizations and abstractions about the lesson:

• Conclude the lesson by asking learners good questions that will help them crystallize their learning so they can declare knowledge and demonstrate their skills.

H. Finding practical applications of concepts and skills in daily living:

• To help students appreciate and value their learning, it's important to connect the lesson to real-life situations. Here are two examples of finding practical applications of concepts and skills in daily living related to the normal distribution:
• Understanding z-scores: One practical application of understanding z-scores is in standardized testing. Test scores are often reported in terms of a student's z-score, which indicates how many standard deviations the student's score is from the mean. This allows us to compare the student's performance to the performance of other students who took the same test, even if the tests were different. Understanding z-scores can also be useful in fields like finance, where investors use z-scores to determine the likelihood of a particular stock performing well or poorly.
• Quality control: Another practical application of the normal distribution is in quality control. Many manufacturing processes produce products with normal distributions of values for certain characteristics, like weight or length. By measuring a sample of products and calculating the mean and standard deviation, manufacturers can determine if the process is within acceptable limits of quality. If the process produces products that fall outside of those limits, adjustments can be made to improve quality and reduce waste.

I. Evaluation of Learning:

1. What is the standard deviation of the standard normal distribution?

A. 0

B. 1

C. 2

D. It depends on the mean

Answer: B

2. What is the area under the standard normal curve to the left of the mean?

A. 0

B. 0.25

C. 0.5

D. 1

Answer: C

3. What is the area under the standard normal curve to the right of the mean?

A. 0

B. 0.25

C. 0.5

D. 1

Answer: A

4. What is the area under the standard normal curve between z = -1 and z = 1?

A. 0

B. 0.25

C. 0.5

D. 1

Answer: C

5. What is the area under the standard normal curve between z = -2 and z = 2?

A. 0

B. 0.25

C. 0.5

D. 1

Answer: D

J. Additional activities for application or remediation:

• Have students research and find real-world examples of how the normal distribution and standard normal distribution are used in different fields such as finance, engineering, or healthcare. Then, have them present their findings in a creative way such as a poster or presentation.

(alert-passed) The lesson plan can be adjusted based on the grade level and the available resources. The teacher may also use different strategies to achieve the objectives.