Here are the answers to the quiz questions:
I.
1. Area = 0.4165 - 0.0253 = 0.3912
2. Area = 0.9646
3. Area = 0.3275
II.
[Sketches the two normal curves described]
The first curve is centered at 15 with width determined by σ of 4. The second curve is centered at 25 with the same width determined by σ of 4.
III.
One real-life situation where a normal distribution can be used is to model human height in a population. Since most people's heights cluster around an average with decreasing frequencies further from the average in both directions, height follows an approximate
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Chapter 6: Normal Probability Distribution
6.1: The Standard Normal Distribution
Discusses on how to determine the area under the normal curve using the z-table. Discusses the skewness and kurtosis of the curve. It includes examples how to determine the area below, above, between, or the end-tails.
Module Five Normal Distributions & Hypothesis TestingTop of F.docxroushhsiu
Module Five: Normal Distributions & Hypothesis Testing
Top of Form
Bottom of Form
·
Introduction & Goals
This week's investigations introduce and explore one of the most common distributions (one you may be familiar with): the Normal Distribution. In our explorations of the distribution and its associated curve, we will revisit the question of "What is typical?" and look at the likelihood (probability) that certain observations would occur in a given population with a variable that is normally distributed. We will apply our work with Normal Distributions to briefly explore some big concepts of inferential statistics, including the Central Limit Theorem and Hypothesis Testing. There are a lot of new ideas in this week’s work. This week is more exploratory in nature.
Goals:
· Explore the Empirical Rule
· Become familiar with the normal curve as a mathematical model, its applications and limitations
· Calculate z-scores & explain what they mean
· Use technology to calculate normal probabilities
· Determine the statistical significance of an observed difference in two means
· Use technology to perform a hypothesis test comparing means (z-test) and interpret its meaning
· Use technology to perform a hypothesis test comparing means (t-test) (optional)
· Gather data for Comparative Study Final Project.
·
DoW #5: The SAT & The ACT
Two Common Tests for college admission are the SAT (Scholastic Aptitude Test) and the ACT (American College Test). The scores for these tests are scaled so that they follow a normal distribution.
· The SAT reported that its scores were normally distributed with a mean μ=896 and a standard deviation σ=174
· The ACT reported that its scores were normally distributed with a mean μ=20.6 and a standard deviation σ=5.2.
We have two questions to consider for this week’s DoW:
2. A high school student Bobby takes both of these tests. On the SAT, he achieves a score of 1080. On the ACT, he achieves a score of 30. He cannot decide which score is the better one to send with his college applications.
. Question: Which test score is the stronger score to send to his colleges?
· A hypothetical group called SAT Prep claims that students who take their SAT Preparatory course score higher on the SAT than the general population. To support their claim, they site a study in which a random sample of 50 SAT Prep students had a mean SAT score of 1000. They claim that since this mean is higher than the known mean of 896 for all SAT scores, their program must improve SAT scores.
. Question: Is this difference in the mean scores statistically significant? Does SAT Prep truly improve SAT Scores?
.
Investigation 1: What is Normal?
One reason for gathering data is to see which observations are most likely. For instance, when we looked at the raisin data in DoW #3, we were looking to see what the most likely number of raisins was for each brand of raisins. We cannot ever be certain of the exact number of raisins in a box (because it varies) ...
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 6: Normal Probability Distribution
6.2: Real Applications of Normal Distributions
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 6: Normal Probability Distribution
6.1: The Standard Normal Distribution
Discusses on how to determine the area under the normal curve using the z-table. Discusses the skewness and kurtosis of the curve. It includes examples how to determine the area below, above, between, or the end-tails.
Module Five Normal Distributions & Hypothesis TestingTop of F.docxroushhsiu
Module Five: Normal Distributions & Hypothesis Testing
Top of Form
Bottom of Form
·
Introduction & Goals
This week's investigations introduce and explore one of the most common distributions (one you may be familiar with): the Normal Distribution. In our explorations of the distribution and its associated curve, we will revisit the question of "What is typical?" and look at the likelihood (probability) that certain observations would occur in a given population with a variable that is normally distributed. We will apply our work with Normal Distributions to briefly explore some big concepts of inferential statistics, including the Central Limit Theorem and Hypothesis Testing. There are a lot of new ideas in this week’s work. This week is more exploratory in nature.
Goals:
· Explore the Empirical Rule
· Become familiar with the normal curve as a mathematical model, its applications and limitations
· Calculate z-scores & explain what they mean
· Use technology to calculate normal probabilities
· Determine the statistical significance of an observed difference in two means
· Use technology to perform a hypothesis test comparing means (z-test) and interpret its meaning
· Use technology to perform a hypothesis test comparing means (t-test) (optional)
· Gather data for Comparative Study Final Project.
·
DoW #5: The SAT & The ACT
Two Common Tests for college admission are the SAT (Scholastic Aptitude Test) and the ACT (American College Test). The scores for these tests are scaled so that they follow a normal distribution.
· The SAT reported that its scores were normally distributed with a mean μ=896 and a standard deviation σ=174
· The ACT reported that its scores were normally distributed with a mean μ=20.6 and a standard deviation σ=5.2.
We have two questions to consider for this week’s DoW:
2. A high school student Bobby takes both of these tests. On the SAT, he achieves a score of 1080. On the ACT, he achieves a score of 30. He cannot decide which score is the better one to send with his college applications.
. Question: Which test score is the stronger score to send to his colleges?
· A hypothetical group called SAT Prep claims that students who take their SAT Preparatory course score higher on the SAT than the general population. To support their claim, they site a study in which a random sample of 50 SAT Prep students had a mean SAT score of 1000. They claim that since this mean is higher than the known mean of 896 for all SAT scores, their program must improve SAT scores.
. Question: Is this difference in the mean scores statistically significant? Does SAT Prep truly improve SAT Scores?
.
Investigation 1: What is Normal?
One reason for gathering data is to see which observations are most likely. For instance, when we looked at the raisin data in DoW #3, we were looking to see what the most likely number of raisins was for each brand of raisins. We cannot ever be certain of the exact number of raisins in a box (because it varies) ...
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 6: Normal Probability Distribution
6.2: Real Applications of Normal Distributions
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
MATATAG CURRICULUM: ASSESSING THE READINESS OF ELEM. PUBLIC SCHOOL TEACHERS I...NelTorrente
In this research, it concludes that while the readiness of teachers in Caloocan City to implement the MATATAG Curriculum is generally positive, targeted efforts in professional development, resource distribution, support networks, and comprehensive preparation can address the existing gaps and ensure successful curriculum implementation.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
11. z
Normal Distribution is
also called as
Gaussian Distribution.
It is the probability of
continuous random
variable and consider
as the most
important curve in
statistics.
14. Properties of Normal
Curve.
1.The distribution curve is bell
shaped.
2.The curve is symmetrical to
its center, the mean.
3.The mean, median and
mode coincide at the center.
15. Properties of Normal
Curve.
3. The width of the curve is determined
by the standard deviation of the
distribution.
4. The curve is asymptotic to the
horizontal axis.
5. The area under the curve is 1, thus
it represents the probability or
proportion, or percentage associated
with specific sets of measurements
values.
16. Normal distribution is determined by two
parameters: the mean and the standard
deviation.
1. Mean Value
2. Standard Deviation Value
17. z
z
Empirical Rule referred to as the 68-
95-99.7% Rule. It tells that for a
normally distributed variable the
following are true.
Distribution Area Under The Normal Curve
18. z
Approximately 68% of the data lie within 1 standard
deviation of the mean. Pr (μ-𝜎<X> μ-𝜎), this is the
formula for getting range and interval of the normal
distribution.
19. z
Approximately 95% of the data lie within 2 standard
deviations of mean. Pr (μ-2𝜎 <X> μ-2𝜎 ), this is the
formula for getting range and interval of the normal
distribution.
20. z
Approximately 99.7% of the lie within 3 standard
deviations of the mean. Pr (μ-2𝜎<X> μ-2𝜎), this is the
formula for getting range and interval of the normal
distribution.
21. z
z
Example 1. What is the
frequency and relative
frequency of babies’
weight that are within;
a. What is the frequency
or percentage of one
standard deviation from
mean.
b. What is the frequency
or percentage of two
standard deviation from
mean.
4.94 4.69 5.26 7.29 7.19 9.47 6.61 5.84 6.83
3.45 2.93 6.38 4.38 6.76 9.02 8.47 6.80 6.40
8.60 3.99 7.68 2.24 5.32 6.24 6.29 5.63 5.37
5.26 7.35 6.11 7.34 5.87 6.56 6.18 7.35 4.21
24. z
z
a. What is the
frequency or percentage
of one standard
deviation from mean.
Solution:
Step 1. Draw a normal
Curve.
Step 2. In the middle of
the curve, plot
the value of the
mean which is 6.11.
6.11
25. z
z
Step 3. The value of
our standard deviation
will become our interval
in the normal
distribution.
1.22 2.85 4.48 6.11 7.74 9.37 11
When you are going to
the right starting in
the middle, mean plus
the standard deviation
meanwhile when you
are going to the left of
the curve standard
deviation is subtracted
from the mean.
26. z Step 4. Since the question is
frequency of one standard deviation
from the mean, we are in the empirical
rule 68% which ranges to 4.48 to
7.74, now we are going to count.
28. z
z
b. What is the
frequency or
percentage of two
standard deviation
from mean.
6.11
Step 1. Draw a
normal Curve.
Step 2. In the
middle of the curve,
plot the value of the
mean which is 6.11.
29. z
z
Step 3. The value of
our standard deviation
will become our interval
in the normal
distribution. 1.22 2.85 4.48 6.11 7.74 9.37 11
Step 4. Since the
question is frequency of
two standard deviation
from the mean, we are
in the empirical rule
95% which ranges to
2.85 to 9.37, now what
is the next thing to do?
35. z
z
The Standard Normal Distribution
Standard Normal Curve is a normal probability
distribution that has a μ= 0 and 𝜎=1.
-3 -2 -1 0 1 2 3
z-score
36. z The letter Z is used to denote
the standard normal random
variable. The specific value of
the random variable z is called
the z-score. The Table of Area
Under the Normal Standard
Curve is also known as the Z-
table. It is where you are going
to look for the value of random
variable z or the z-core.
42. z
Let’s try
this !
1. Anna is planning to enroll in MSU
taking up Bachelor of Science in Civil
Engineering. The average academic
performance of all the students 80 and
a standard deviation of 5, it follows a
normal distribution.
a. Sketch a Normal Curve using
Empirical Rule and describe the
curves.
2. Find the area between z=1.7 and z=2
43. z
Let's have a short quiz.
Instruction: Answer the following questions and
make sure your writings clear and readable.
I. Find the area under the normal curve in
each of the following cases.
1. Find the Area between z= -1.36
and z=2.25.
2. To the right of z=1.85
3. To the left z=-0.45
44. z
II. Sketch a normal curve.
1. Mean of 15 and a standard deviation of 4.
On same axis, sketch another curve that has a
mean of 25 and a standard deviation of 4.
Describe the two random curves.
III. Essay
1. State a real-life situation that a normal curve
distribution can be used.