School Dalaguete National High Grade Level 11

School
Teacher Ruena A. Rosales Learning Area Statistic and
Probability
Duration 1 hour Quarter 4th Quarter
Daily Lesson Plan

I. OBJECTIVES:
A. Content Standards The learner demonstrates understanding of key concepts of estimation of a
population mean and population proportion.
B. Performance Standards The learner is able to estimate the population mean and population proportion to
make sound inferences in real-life problems in different disciplines.
C. Learning Competencies & 1. find the mean and variance of the sampling distribution of the sample mean
(M11/12SP-IIId-5) ; and
2. define the sampling distribution of the sample mean for normal population
when the variance is: (a) known; (b) unknown (M11/12SP-IIIe-1) .

Objectives At the end of this lesson, students should be able to:

1. demonstrates understanding of key concepts of sampling and sampling
distributions of the sample mean
2. apply suitable sampling and sampling distributions of the sample
mean to solve real – life problems in different disciplines.
3. defines the sampling distribution of the sample mean for normal
population when the variance is (a) known and (b) unknown.
II. SUBJECT MATTER:
A. Topic: Sampling Distribution of the Sample Mean for Normal Population When-the
Variance is (a) Known and (b) Unknown

B. References: A.MELCs and Conceptual Math & Beyond (Statistics and Probability) by Jose
M. Ocampo Jr. and Wilmer G.Marquez pages 86 – 108
https://www.youtube.com/watch?v=g1I2C0HW7qg

C. Materials: PowerPoint Presentation, Laptop, and TV

Skills Acquired Identifying

Values Integration Display cooperation during the activity.
III. LEARNING PROCEDURE
A. Preliminary Activities
1. Prayer The teacher starts the lesson with a prayer.

2. Checking of The teacher checks the attendance by telling the secretary of the class to record
attendance the names of the students who were absent.

3. Classroom The teacher instructs the class to arrange the chairs and pick up the pieces of
management garbage under the chairs.

4. Review The teacher asks students about the tackled previous lesson. What is the formula
to use in:
A. Compute the population mean of the sampling distribution.
B. Compute the variance of the population
C. Compute the standard deviation of the population.
D. Compute the population mean of the sampling distributions of the sample
means.
E. Compute the population variance of the sampling distribution of the sample
means.
F. Compute the standard deviation of the sampling distribution of the sample
means.

B. Lesson Proper
1. Activity  The students will perform the activity “Answer Mo, Show Mo!”. In this
activity the student will solve the given problems below by group.
 After the allotted time, they will raise their written answers. The group with
the highest number of points after five rounds will win the game.
1. A fish catch (expressed in kilograms) consists of five values (15, 17, 9, 12,
and 13). A sample size 2 is to be taken from this population.
 A. Compute the population mean of the sampling distribution.
B. Compute the variance of the population
C. Compute the standard deviation of the population.
D. Compute the population mean of the sampling distributions of the sample
means.
E. Compute the population variance of the sampling distribution of the sample
means.
F. Compute the standard deviation of the sampling distribution of the sample
means.
2. Analysis Process Questions:
 Based on the activities, does the population variance is known? Or
Unknown?
 Based on the activities we had in a while ago, do you know now what is our
lesson for today?
3. Abstraction Today we will tackle about Sampling Distribution of the Sample Mean for
Normal Population When-the Variance is (a) Known and (b) Unknown.

Remember this: When population variance is known:

 The population has a mean and variance 
 The distribution of the sample mean is (at least approximately)normal; and
 Standard error of the mean SEM = σ/√n To determine the probability of a
certain event, we can use the z-distribution by transforming the mean of the
sample data to an approximately normal variable z, using the relation.

This distribution is best applied for large sample sizes, say n≥30.
When population variance is unknown: 
 The standard error of the mean is SE = s / √n . To estimate the population
parameters, we can use the t- distribution by using the formula.

Remember that we use the t-distribution for small sample size, say n<30.

Example:
1. Consider a population consisting of 1,2,3,4,5,8,9 and 11. Samples of size 3
are drawn from this population. 
 Given: N=9 and n=3 
 Sampling distribution when the variance is known. 
 The standard error formula:SEM = σ/√n
2. Given the population mean of 12, and a sample standard deviation of 3 in a
sample size of 125. 
 Given: μ=12, s=3, and n=125 
 The population variance is unknown 
 The standard error formula:SE = s / √n
3. A population composed of 10 items whose measurements are
12,1115,8,20,23,18,13,22 and 10. Samples of 6 items are drawn at random
without replacement. 
 Given: N=10 and n=6 
 Sampling distribution when the variance is known. 
 The standard error formula:SEM = σ/√n
4. An SHS teacher claims that the average time it takes a group of students to
complete the mathematics examination is 50.5 minutes with a variance of 17.64 .
She randomly selected 45 students and found to have a mean of 52 minutes and a
standard deviation of 3.5 minutes. She then used the z-distribution to find out if
the group can complete the exam faster than the population. 
 Given: μ=50.5, =17.64, n=45, x̄ =52, and s=3.5 
 The population variance is known 
 The standard error formula:SEM = σ/√n
5. A manufacturer of light bulbs produces bulbs that last a mean of 800 hours
 with a standard deviation of 100 hours. To assess the claim of the manufacturer, a
random sample of 12 of these bulbs was tested and found to have a mean of 790
hours. He then used the test variate 
 Given: μ=800, σ=100, n=12, x̄ =790 
 The standard error formula:SE = s / √n
4. Application Instruction: Read and analyze the following situations. Determine whether
the following statements have a known or unknown population variance.
1. Consider a population consisting of 1,2,3,4 and 5. Samples of size 2 are
drawn from this population. known
2. Given: μ =20 s=6 n=15 unkown
3. Test scores are normally distributed with standard deviation σ=12 points.
You wish to determine the μ test scores of all students in Masaya National High
School by taking a random sample of 18 students. known
4. The general weighted average (GWA) of grade 7 applicants for admission in
LNHS over the past 7 years has been consistently μ=91.88. This year a sample
data of the applicant’s GWA are 96,90,92,93,96,95,91,92,90, and 93. unknown
5. A finite population composed of six items whose values are 2,3,6,7,8 and 10.
Samples of 3 items are drawn at random without replacement. known
IV. EVALUATION Direction: Read and analyze each item carefully. Choose the letter that
corresponds to your answer.

1. This distribution is used to estimate population parameters when the

population variance is unknown, and the sample size is less than 30.
A. Z-Distribution B.t-Distribution C.Chi-Square Distribution D.Pearson
Correlation Coefficient
2. Which of the following notations is used for the standard deviation of the
sampling distribution of the sample sample mean to an approximately standard
normal variable Z when the population variance is known?
A. σ B. σ² C. σ/√n D. s/√n
3. The mean weight of two thousand (2000) 11-year-old children is 35
kilograms with a standard deviation of 5 kilograms. Samples of 25 children were
selected and the mean weight of this group was found to be 34 kilograms with a
standard deviation of 3 kilograms. What condition of the sampling distribution of
the sample mean for normal population manifests in the situation?
A. Population variance is known
B. Population variance is unknown
C. Sample standard deviation is small
D. Sample standard deviation is large
4. Which of the following formulas is used to calculate the standard deviation of
the sampling distribution of the sample mean when the population standard
deviation is unknown?
A. σ / √n B. s² / n C. s / √n D. σ² / n
5. A population consists 1, 9, 2, 12, 8, 7, and 10. Suppose samples of size 5 are
drawn from this population. This situation is an example of the sampling
distribution of the sample mean for a normal population wherein population
variance is______. A. The variance of the sample means
B. The variance of the original population
C. The variance of the population divided by the sample size
D. The square root of the population variance
6. Suppose the manager of a Jollibee Corp. wishes to know whether their
chicken packaging machine still packs accurately after 6 months of use. The
machine was rated to pack 1,500-gram pack of chicken with a standard deviation
of 30 grams. The statistician tests a sample of 40 packs to test the accuracy of the
machine. What example of sampling distribution of the sample mean for normal
population portrays the situation?
A. variance is known B. variance is unknown
B. standard deviation is small D. standard deviation is large
7. This distribution is used to determine the probability of an event by
transforming the mean of the sample to an approximately standard normal
variable if the population variance is known and sample size is greater than 30.
A. t-Distribution B. Z-Distribution
B. Chi-Square Distribution D. Pearson Correlation Coefficient
8. Which of the following formulas is used to calculate the standard deviation of
the sampling distribution of the sample mean when the population standard
deviation is given?
A. σ² / n B. σ / √n C. s / √n D. √σ / n
9. Given μ=15, σ=5, ?? =12.8 and n=100. This is an example of the sampling
distribution of the sample mean for a normal population when the population
 variance is _______.
A. unknown C. large B. known D. Small
10. Given a population consisting of the following measurements (x) 2, 8, 11,
7, 𝑎𝑛𝑑 3. Suppose that samples of size 2 are drawn from the population.
Compute the mean and variance of the sampling distribution of the sample mean.
A) Mean = 6.2, Variance = 10.56
B) Mean = 6.2, Variance = 8.40
C) Mean = 5.8, Variance = 10.56
D) Mean = 5.8, Variance = 8.40
11. This distribution is used to determine the probability of an event by
transforming the mean of the sample to an approximately standard normal
variable when the population variance is given.
A. t-Distribution B. Z-Distribution
B. Chi-Square Distribution D. Pearson Correlation Coefficient
12. Which of the following notations is used for the mean of the population?

13. A population consists 11, 19, 22, 2, 8, 9, and 15.Suppose samples of 2 are
drawn from this population. This situation is an example of the sampling
distribution of the sample mean for a normal population with population variance
is __________. A.unknown B. large C. known D. Small
14. The average family income in the Philippines in 2019 was P22,250 with a
standard deviation of P1,250. In a certain municipality, a sample of 50 families
had an average income of P25,000. This situation is about the sampling
distribution of the sample mean where the population ________.
A. Variance is unknown B. Standard deviation is unknown
B. Variance is known D. Mean is unknown
15. Given 𝜇= 54.2, 𝜎 = 7.8, ?? =60.2 and 𝑛 = 76. This is an example of the
sampling distribution of the sample mean for a normal population when the
population variance is _______.
A. unknown C. large B. known D. small
V. ASSIGNMENT For your assignment, do advance research about Central Limit Theorem.

Prepared by:

Lynch Denver Tugbong Assessed by: RUENA ROSALES

________________________
UV- Dalaguete Student Intern

Date:___________________