1. The probability that a random sample of 50 normal men will yield a mean serum iron level between 115 and 125 micrograms per 100 ml is approximately 98.18%.
2. The mean of the sampling distribution for the mean serum cholesterol level of US females based on samples of size 50 is 204 mg/dl. The standard error is 6.22 mg/dl.
3. The probability that a resident consumes at most 3 types of food is 0.7675 or 76.75%.
Statistics is the science of dealing with numbers.
It is used for collection, summarization, presentation and analysis of data.
Statistics provides a way of organizing data to get information on a wider and more formal (objective) basis than relying on personal experience (subjective).
Statistics is the science of dealing with numbers.
It is used for collection, summarization, presentation and analysis of data.
Statistics provides a way of organizing data to get information on a wider and more formal (objective) basis than relying on personal experience (subjective).
This presentation gives you a brief idea;
-definition of frequency distribution
- types of frequency distribution
-types of charts used in the distribution
-a problem on creating types of distribution
-advantages and limitations of the distribution
OBJECTIVES:
Run the test of hypothesis for mean difference using paired samples. Construct a confidence interval for the difference in population means using paired samples.
Observation of interest will be the difference in the readings
before and after intervention called paired difference observation.
Paired t test:
A paired t-test is used to compare two means where you have two samples in which observations in one sample can be paired with observations in the other sample.
Examples of where this might occur are:
Before-and-after observations on the same subjects (e.g. students’ test
results before and after a particular module or course).
A comparison of two different methods of measurement or two different treatments where the measurements/treatments are applied to the same subjects (e.g. blood pressure measurements using a sphygmomanometer and a dynamap).
When there is a relationship between the groups, such as identical twins.
This test is concerned with the pair-wise differences
between sets of data.
This means that each data point in one group has a related data point in the other group (groups always have equal numbers).
ASSUMPTIONS:
The sample or samples are randomly selected
The sample data are dependent
The distribution of differences is approximately normally
distributed.
Note: The under root is onto the entire numerator and denominator, so you should take the root after solving it entirely
where “t” has (n-1) degrees of freedom and “n” is
the total number of pairs.
This presentation educates you about T-Test, Key takeways, Assumptions for Performing a t-test, Types of t-tests, One sample t-test, Independent two-sample t-test and Paired sample t-test.
For more topics Stay tuned with Learnbay
Topic: Frequency Distribution
Student Name: Abdul Hafeez
Class: B.Ed. (Hons) Elementary
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
At the end of this lecture, the student should be able to:
1. understand structure of research study appropriate for independent-measures t hypothesis test
2. test between two populations or two treatments using independent measures t statistics
3. understand how to evaluate the assumptions underlying this test
This presentation gives you a brief idea;
-definition of frequency distribution
- types of frequency distribution
-types of charts used in the distribution
-a problem on creating types of distribution
-advantages and limitations of the distribution
OBJECTIVES:
Run the test of hypothesis for mean difference using paired samples. Construct a confidence interval for the difference in population means using paired samples.
Observation of interest will be the difference in the readings
before and after intervention called paired difference observation.
Paired t test:
A paired t-test is used to compare two means where you have two samples in which observations in one sample can be paired with observations in the other sample.
Examples of where this might occur are:
Before-and-after observations on the same subjects (e.g. students’ test
results before and after a particular module or course).
A comparison of two different methods of measurement or two different treatments where the measurements/treatments are applied to the same subjects (e.g. blood pressure measurements using a sphygmomanometer and a dynamap).
When there is a relationship between the groups, such as identical twins.
This test is concerned with the pair-wise differences
between sets of data.
This means that each data point in one group has a related data point in the other group (groups always have equal numbers).
ASSUMPTIONS:
The sample or samples are randomly selected
The sample data are dependent
The distribution of differences is approximately normally
distributed.
Note: The under root is onto the entire numerator and denominator, so you should take the root after solving it entirely
where “t” has (n-1) degrees of freedom and “n” is
the total number of pairs.
This presentation educates you about T-Test, Key takeways, Assumptions for Performing a t-test, Types of t-tests, One sample t-test, Independent two-sample t-test and Paired sample t-test.
For more topics Stay tuned with Learnbay
Topic: Frequency Distribution
Student Name: Abdul Hafeez
Class: B.Ed. (Hons) Elementary
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
At the end of this lecture, the student should be able to:
1. understand structure of research study appropriate for independent-measures t hypothesis test
2. test between two populations or two treatments using independent measures t statistics
3. understand how to evaluate the assumptions underlying this test
What is statistical analysis? It's the science of collecting, exploring and presenting large amounts of data to discover underlying patterns and trends. Statistics are applied every day – in research, industry and government – to become more scientific about decisions that need to be made.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 7: Estimating Parameters and Determining Sample Sizes
7.2: Estimating a Population Mean
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 7: Estimating Parameters and Determining Sample Sizes
7.2: Estimating a Population Mean
Sex linked describes the sex-specific patterns of inheritance and presentation when a gene mutation is present on a sex chromosome rather than a non-sex chromosome. In humans, these are termed X-linked recessive, X-linked dominant and Y-linked.
Connexins (Cx) (TC# 1.A.24), or gap junction proteins, are structurally related transmembrane proteins that assemble to form vertebrate gap junctions. An entirely different family of proteins, the innexins, form gap junctions in invertebrates.[1] Each gap junction is composed of two hemichannels, or connexons, which consist of homo- or heterohexameric arrays of connexins, and the connexon in one plasma membrane docks end-to-end with a connexon in the membrane of a closely opposed cell. The hemichannel is made of six connexin subunits, each of which consist of four transmembrane segments. Gap junctions are essential for many physiological processes, such as the coordinated depolarization of cardiac muscle, proper embryonic development, and the conducted response in microvasculature. For this reason, mutations in connexin-encoding genes can lead to functional and developmental abnormalities.
Eicosanoids are signaling molecules made by the enzymatic or non-enzymatic oxidation of arachidonic acid or other polyunsaturated fatty acids (PUFAs) that are, similar to arachidonic acid, 20 carbon units in length. Eicosanoids are a sub-category of oxylipins, i.e. oxidized fatty acids of diverse carbon units in length, and are distinguished from other oxylipins by their overwhelming importance as cell signaling molecules. Eicosanoids function in diverse physiological systems and pathological processes such as: mounting or inhibiting inflammation, allergy, fever and other immune responses; regulating the abortion of pregnancy and normal childbirth; contributing to the perception of pain; regulating cell growth; controlling blood pressure; and modulating the regional flow of blood to tissues. In performing these roles, eicosanoids most often act as autocrine signaling agents to impact their cells of origin or as paracrine signaling agents to impact cells in the proximity of their cells of origin. Eicosanoids may also act as endocrine agents to control the function of distant cells.
Cerebral circulation is the movement of blood through a network of cerebral arteries and veins supplying the brain. The rate of cerebral blood flow in an adult human is typically 750 milliliters per minute, or about 15% of cardiac output. Arteries deliver oxygenated blood, glucose and other nutrients to the brain. Veins carry "used or spent" blood back to the heart, to remove carbon dioxide, lactic acid, and other metabolic products.[1] Because the brain would quickly suffer damage from any stoppage in blood supply, the cerebral circulatory system has safeguards including autoregulation of the blood vessels. The failure of these safeguards may result in a stroke. The volume of blood in circulation is called the cerebral blood flow. Sudden intense accelerations change the gravitational forces perceived by bodies and can severely impair cerebral circulation and normal functions to the point of becoming serious life-threatening conditions.
Ecosystem is system formed by the interaction of a community of organisms with their physical environment.
Ecosystem can be natural or artificial.
Ecosystem has both abiotic and biotic components.
Ecosystem has primary, secondary and tertiary function.
Human social systems and ecosystems are complex adaptive systems
Ergonomics is the study of people in their working environment.
Cushing's syndrome is the pool of signs and symptoms due to extended exposure to glucocorticoids such as cortisol.
Signs and symptoms may include high blood pressure, abdominal obesity but with thin arms and legs, reddish stretch marks, a round red face, a fat lump between the shoulders, weak muscles, weak bones, acne, and fragile skin that heals poorly.
Women may have more hair and irregular menstruation. Occasionally there may be changes in mood, headaches, and a chronic feeling of tiredness.
Usual onset: 20 – 50 years
According to UNESCO Constructivism is learning theory which places the learner at the center of the educational process on the understanding that the learner actively constructs knowledge rather than passively receiving it.
According to Brader - Araje and Jones (2002), Constructivism can be defined as “the idea that development of understanding requires the learner to actively engage in meaning-making”.
Electroencephalography (EEG): an electrophysiological monitoring method to re...Habtemariam Mulugeta
Electroencephalography (EEG) is an electrophysiological monitoring method to record electrical activity of the brain.
It is typically noninvasive, with the electrodes placed along the scalp, although invasive electrodes are sometimes used, as in electrocorticography.
EEG measures voltage fluctuations resulting from ionic current within the neurons of the brain.
As Hall says; “To look at and listen to self is often too difficult without the help of a significant figure (nurturer) who has learned how to hold up a mirror and sounding board to invite the behaver to look and listen to himself. If he accepts the invitation, he will explore the concerns in his acts and as he listens to his exploration through the reflection of the nurse, he may uncover in sequence his difficulties, the problem area, his problem, and eventually the threat which is dictating his out-of-control behavior.”
The musculoskeletal system consists of the muscles, tendons, bones and cartilage together with the joints
The primary function of which is to produce skeletal movements
Knee anatomy and clinical tests 2024.pdfvimalpl1234
This includes all relevant anatomy and clinical tests compiled from standard textbooks, Campbell,netter etc..It is comprehensive and best suited for orthopaedicians and orthopaedic residents.
Lung Cancer: Artificial Intelligence, Synergetics, Complex System Analysis, S...Oleg Kshivets
RESULTS: Overall life span (LS) was 2252.1±1742.5 days and cumulative 5-year survival (5YS) reached 73.2%, 10 years – 64.8%, 20 years – 42.5%. 513 LCP lived more than 5 years (LS=3124.6±1525.6 days), 148 LCP – more than 10 years (LS=5054.4±1504.1 days).199 LCP died because of LC (LS=562.7±374.5 days). 5YS of LCP after bi/lobectomies was significantly superior in comparison with LCP after pneumonectomies (78.1% vs.63.7%, P=0.00001 by log-rank test). AT significantly improved 5YS (66.3% vs. 34.8%) (P=0.00000 by log-rank test) only for LCP with N1-2. Cox modeling displayed that 5YS of LCP significantly depended on: phase transition (PT) early-invasive LC in terms of synergetics, PT N0—N12, cell ratio factors (ratio between cancer cells- CC and blood cells subpopulations), G1-3, histology, glucose, AT, blood cell circuit, prothrombin index, heparin tolerance, recalcification time (P=0.000-0.038). Neural networks, genetic algorithm selection and bootstrap simulation revealed relationships between 5YS and PT early-invasive LC (rank=1), PT N0—N12 (rank=2), thrombocytes/CC (3), erythrocytes/CC (4), eosinophils/CC (5), healthy cells/CC (6), lymphocytes/CC (7), segmented neutrophils/CC (8), stick neutrophils/CC (9), monocytes/CC (10); leucocytes/CC (11). Correct prediction of 5YS was 100% by neural networks computing (area under ROC curve=1.0; error=0.0).
CONCLUSIONS: 5YS of LCP after radical procedures significantly depended on: 1) PT early-invasive cancer; 2) PT N0--N12; 3) cell ratio factors; 4) blood cell circuit; 5) biochemical factors; 6) hemostasis system; 7) AT; 8) LC characteristics; 9) LC cell dynamics; 10) surgery type: lobectomy/pneumonectomy; 11) anthropometric data. Optimal diagnosis and treatment strategies for LC are: 1) screening and early detection of LC; 2) availability of experienced thoracic surgeons because of complexity of radical procedures; 3) aggressive en block surgery and adequate lymph node dissection for completeness; 4) precise prediction; 5) adjuvant chemoimmunoradiotherapy for LCP with unfavorable prognosis.
TEST BANK for Operations Management, 14th Edition by William J. Stevenson, Ve...kevinkariuki227
TEST BANK for Operations Management, 14th Edition by William J. Stevenson, Verified Chapters 1 - 19, Complete Newest Version.pdf
TEST BANK for Operations Management, 14th Edition by William J. Stevenson, Verified Chapters 1 - 19, Complete Newest Version.pdf
Prix Galien International 2024 Forum ProgramLevi Shapiro
June 20, 2024, Prix Galien International and Jerusalem Ethics Forum in ROME. Detailed agenda including panels:
- ADVANCES IN CARDIOLOGY: A NEW PARADIGM IS COMING
- WOMEN’S HEALTH: FERTILITY PRESERVATION
- WHAT’S NEW IN THE TREATMENT OF INFECTIOUS,
ONCOLOGICAL AND INFLAMMATORY SKIN DISEASES?
- ARTIFICIAL INTELLIGENCE AND ETHICS
- GENE THERAPY
- BEYOND BORDERS: GLOBAL INITIATIVES FOR DEMOCRATIZING LIFE SCIENCE TECHNOLOGIES AND PROMOTING ACCESS TO HEALTHCARE
- ETHICAL CHALLENGES IN LIFE SCIENCES
- Prix Galien International Awards Ceremony
Title: Sense of Smell
Presenter: Dr. Faiza, Assistant Professor of Physiology
Qualifications:
MBBS (Best Graduate, AIMC Lahore)
FCPS Physiology
ICMT, CHPE, DHPE (STMU)
MPH (GC University, Faisalabad)
MBA (Virtual University of Pakistan)
Learning Objectives:
Describe the primary categories of smells and the concept of odor blindness.
Explain the structure and location of the olfactory membrane and mucosa, including the types and roles of cells involved in olfaction.
Describe the pathway and mechanisms of olfactory signal transmission from the olfactory receptors to the brain.
Illustrate the biochemical cascade triggered by odorant binding to olfactory receptors, including the role of G-proteins and second messengers in generating an action potential.
Identify different types of olfactory disorders such as anosmia, hyposmia, hyperosmia, and dysosmia, including their potential causes.
Key Topics:
Olfactory Genes:
3% of the human genome accounts for olfactory genes.
400 genes for odorant receptors.
Olfactory Membrane:
Located in the superior part of the nasal cavity.
Medially: Folds downward along the superior septum.
Laterally: Folds over the superior turbinate and upper surface of the middle turbinate.
Total surface area: 5-10 square centimeters.
Olfactory Mucosa:
Olfactory Cells: Bipolar nerve cells derived from the CNS (100 million), with 4-25 olfactory cilia per cell.
Sustentacular Cells: Produce mucus and maintain ionic and molecular environment.
Basal Cells: Replace worn-out olfactory cells with an average lifespan of 1-2 months.
Bowman’s Gland: Secretes mucus.
Stimulation of Olfactory Cells:
Odorant dissolves in mucus and attaches to receptors on olfactory cilia.
Involves a cascade effect through G-proteins and second messengers, leading to depolarization and action potential generation in the olfactory nerve.
Quality of a Good Odorant:
Small (3-20 Carbon atoms), volatile, water-soluble, and lipid-soluble.
Facilitated by odorant-binding proteins in mucus.
Membrane Potential and Action Potential:
Resting membrane potential: -55mV.
Action potential frequency in the olfactory nerve increases with odorant strength.
Adaptation Towards the Sense of Smell:
Rapid adaptation within the first second, with further slow adaptation.
Psychological adaptation greater than receptor adaptation, involving feedback inhibition from the central nervous system.
Primary Sensations of Smell:
Camphoraceous, Musky, Floral, Pepperminty, Ethereal, Pungent, Putrid.
Odor Detection Threshold:
Examples: Hydrogen sulfide (0.0005 ppm), Methyl-mercaptan (0.002 ppm).
Some toxic substances are odorless at lethal concentrations.
Characteristics of Smell:
Odor blindness for single substances due to lack of appropriate receptor protein.
Behavioral and emotional influences of smell.
Transmission of Olfactory Signals:
From olfactory cells to glomeruli in the olfactory bulb, involving lateral inhibition.
Primitive, less old, and new olfactory systems with different path
New Drug Discovery and Development .....NEHA GUPTA
The "New Drug Discovery and Development" process involves the identification, design, testing, and manufacturing of novel pharmaceutical compounds with the aim of introducing new and improved treatments for various medical conditions. This comprehensive endeavor encompasses various stages, including target identification, preclinical studies, clinical trials, regulatory approval, and post-market surveillance. It involves multidisciplinary collaboration among scientists, researchers, clinicians, regulatory experts, and pharmaceutical companies to bring innovative therapies to market and address unmet medical needs.
The prostate is an exocrine gland of the male mammalian reproductive system
It is a walnut-sized gland that forms part of the male reproductive system and is located in front of the rectum and just below the urinary bladder
Function is to store and secrete a clear, slightly alkaline fluid that constitutes 10-30% of the volume of the seminal fluid that along with the spermatozoa, constitutes semen
A healthy human prostate measures (4cm-vertical, by 3cm-horizontal, 2cm ant-post ).
It surrounds the urethra just below the urinary bladder. It has anterior, median, posterior and two lateral lobes
It’s work is regulated by androgens which are responsible for male sex characteristics
Generalised disease of the prostate due to hormonal derangement which leads to non malignant enlargement of the gland (increase in the number of epithelial cells and stromal tissue)to cause compression of the urethra leading to symptoms (LUTS
micro teaching on communication m.sc nursing.pdfAnurag Sharma
Microteaching is a unique model of practice teaching. It is a viable instrument for the. desired change in the teaching behavior or the behavior potential which, in specified types of real. classroom situations, tends to facilitate the achievement of specified types of objectives.
Recomendações da OMS sobre cuidados maternos e neonatais para uma experiência pós-natal positiva.
Em consonância com os ODS – Objetivos do Desenvolvimento Sustentável e a Estratégia Global para a Saúde das Mulheres, Crianças e Adolescentes, e aplicando uma abordagem baseada nos direitos humanos, os esforços de cuidados pós-natais devem expandir-se para além da cobertura e da simples sobrevivência, de modo a incluir cuidados de qualidade.
Estas diretrizes visam melhorar a qualidade dos cuidados pós-natais essenciais e de rotina prestados às mulheres e aos recém-nascidos, com o objetivo final de melhorar a saúde e o bem-estar materno e neonatal.
Uma “experiência pós-natal positiva” é um resultado importante para todas as mulheres que dão à luz e para os seus recém-nascidos, estabelecendo as bases para a melhoria da saúde e do bem-estar a curto e longo prazo. Uma experiência pós-natal positiva é definida como aquela em que as mulheres, pessoas que gestam, os recém-nascidos, os casais, os pais, os cuidadores e as famílias recebem informação consistente, garantia e apoio de profissionais de saúde motivados; e onde um sistema de saúde flexível e com recursos reconheça as necessidades das mulheres e dos bebês e respeite o seu contexto cultural.
Estas diretrizes consolidadas apresentam algumas recomendações novas e já bem fundamentadas sobre cuidados pós-natais de rotina para mulheres e neonatos que recebem cuidados no pós-parto em unidades de saúde ou na comunidade, independentemente dos recursos disponíveis.
É fornecido um conjunto abrangente de recomendações para cuidados durante o período puerperal, com ênfase nos cuidados essenciais que todas as mulheres e recém-nascidos devem receber, e com a devida atenção à qualidade dos cuidados; isto é, a entrega e a experiência do cuidado recebido. Estas diretrizes atualizam e ampliam as recomendações da OMS de 2014 sobre cuidados pós-natais da mãe e do recém-nascido e complementam as atuais diretrizes da OMS sobre a gestão de complicações pós-natais.
O estabelecimento da amamentação e o manejo das principais intercorrências é contemplada.
Recomendamos muito.
Vamos discutir essas recomendações no nosso curso de pós-graduação em Aleitamento no Instituto Ciclos.
Esta publicação só está disponível em inglês até o momento.
Prof. Marcus Renato de Carvalho
www.agostodourado.com
- Video recording of this lecture in English language: https://youtu.be/lK81BzxMqdo
- Video recording of this lecture in Arabic language: https://youtu.be/Ve4P0COk9OI
- Link to download the book free: https://nephrotube.blogspot.com/p/nephrotube-nephrology-books.html
- Link to NephroTube website: www.NephroTube.com
- Link to NephroTube social media accounts: https://nephrotube.blogspot.com/p/join-nephrotube-on-social-media.html
263778731218 Abortion Clinic /Pills In Harare ,sisternakatoto
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Report Back from SGO 2024: What’s the Latest in Cervical Cancer?bkling
Are you curious about what’s new in cervical cancer research or unsure what the findings mean? Join Dr. Emily Ko, a gynecologic oncologist at Penn Medicine, to learn about the latest updates from the Society of Gynecologic Oncology (SGO) 2024 Annual Meeting on Women’s Cancer. Dr. Ko will discuss what the research presented at the conference means for you and answer your questions about the new developments.
Tom Selleck Health: A Comprehensive Look at the Iconic Actor’s Wellness Journeygreendigital
Tom Selleck, an enduring figure in Hollywood. has captivated audiences for decades with his rugged charm, iconic moustache. and memorable roles in television and film. From his breakout role as Thomas Magnum in Magnum P.I. to his current portrayal of Frank Reagan in Blue Bloods. Selleck's career has spanned over 50 years. But beyond his professional achievements. fans have often been curious about Tom Selleck Health. especially as he has aged in the public eye.
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Introduction
Many have been interested in Tom Selleck health. not only because of his enduring presence on screen but also because of the challenges. and lifestyle choices he has faced and made over the years. This article delves into the various aspects of Tom Selleck health. exploring his fitness regimen, diet, mental health. and the challenges he has encountered as he ages. We'll look at how he maintains his well-being. the health issues he has faced, and his approach to ageing .
Early Life and Career
Childhood and Athletic Beginnings
Tom Selleck was born on January 29, 1945, in Detroit, Michigan, and grew up in Sherman Oaks, California. From an early age, he was involved in sports, particularly basketball. which played a significant role in his physical development. His athletic pursuits continued into college. where he attended the University of Southern California (USC) on a basketball scholarship. This early involvement in sports laid a strong foundation for his physical health and disciplined lifestyle.
Transition to Acting
Selleck's transition from an athlete to an actor came with its physical demands. His first significant role in "Magnum P.I." required him to perform various stunts and maintain a fit appearance. This role, which he played from 1980 to 1988. necessitated a rigorous fitness routine to meet the show's demands. setting the stage for his long-term commitment to health and wellness.
Fitness Regimen
Workout Routine
Tom Selleck health and fitness regimen has evolved. adapting to his changing roles and age. During his "Magnum, P.I." days. Selleck's workouts were intense and focused on building and maintaining muscle mass. His routine included weightlifting, cardiovascular exercises. and specific training for the stunts he performed on the show.
Selleck adjusted his fitness routine as he aged to suit his body's needs. Today, his workouts focus on maintaining flexibility, strength, and cardiovascular health. He incorporates low-impact exercises such as swimming, walking, and light weightlifting. This balanced approach helps him stay fit without putting undue strain on his joints and muscles.
Importance of Flexibility and Mobility
In recent years, Selleck has emphasized the importance of flexibility and mobility in his fitness regimen. Understanding the natural decline in muscle mass and joint flexibility with age. he includes stretching and yoga in his routine. These practices help prevent injuries, improve posture, and maintain mobilit
Tom Selleck Health: A Comprehensive Look at the Iconic Actor’s Wellness Journey
Biostatistics Assignment
1. COLLEGE OF HEALTH SCIENCE
SCHOOL OF MEDICINE
DEPARTMENT OF MEDICAL PHYSIOLOGY
BIOSTATISTICS ASSIGNMENT
PREPARED BY: HABTEMARIAM MULUGETA
ABATE
ID NO: GSR/2895/14
ADDIS ABABA, ETHIOPIA
3. 1
1. If the mean and standard deviation of serum iron values for healthy men are 120
and 15 micrograms per 100 ml, respectively, what is the probability that a random
sample of 50 normal men will yield a mean between 115 and 125 micrograms per
100 ml?
Given:
µ = 120,
σ = 15,
n = 50,
Mean (𝑋̅)1 = 115 and Mean (𝑋̅)2 = 125
Required:
What is the probability that a random sample of 50 normal men will yield a mean
between 115 and 125 micrograms per 100 ml?
Solution:
As shown in the above picture that we do not know the distribution of serum iron values,
but the sample size is large, so we can apply the Central Limit Theorem for the sample
means. We need to find the p (115≤ x ≤ 125)
4. 2
Therefore, p (115 ≤ 𝑋̅ ≤ 125) = p[
(115 − 120)
15
√50
⁄
] ≤ [
(X
̅− µ)
σ
√𝑛
⁄
] ≤ [
(125 − 120)
15
√50
⁄
]
p (115 ≤ 𝑋̅ ≤ 125) = p[
(115 − 120)
15
√50
⁄
] ≤ 𝑍 ≤ [
(125 − 120)
15
√50
⁄
]
p (115 ≤ 𝑋̅ ≤ 125) = p (−2.357 ≤ 𝑍 ≤ 2.357 )
Since the Z table shows at two decimal places, I approximated the values to two decimal
places. p (115 ≤ 𝑋̅ ≤ 125) = p (-2.36 ≤ Z ≤ 2.36)
p (115 ≤ 𝑋̅ ≤ 125) = p (𝑍 ≤ 2.36 )− 𝑝 (𝑍 ≤ − 2.36)
p (115 ≤ 𝑋̅ ≤ 125) = 0.9909 - 0.0091
p (115 ≤ 𝑋̅ ≤ 125) = 0.9818
Thus, approximately 98.18 % of normal sample will yield a mean between 115 and 125
micrograms per 100 ml.
2. The National Health and Nutrition Examination Survey of 1988–1994 (NHANES III, A-
1) estimated the mean serum cholesterol level for U.S. females aged 20–74 years to be 204
mg/dl. The estimate of the standard deviation was approximately 44. Using these estimates
as the mean x and standard deviation s for the U.S. population, consider the sampling
distribution of the sample mean based on samples of size 50 drawn from women in this age
group. What is the mean of the sampling distribution? The standard error?
Given:
Mean (𝑋̅) = 204
σ = 44,
n = 50,
Required:
What is the mean of the sampling distribution?
The standard error?
5. 3
Solution:
The mean of the sampling distribution 𝑿̅
Mean(𝑋̅) = µ = 204
The standard error of 𝑿̅
S.E =
σ
√n
=
44
√50
= 6.22
Use the following table for question #3 - #6
Variety of food in number (x) Probability of consuming that variety of food (P(X=x))
1 0.4231
2 0.3321
3 0.0123
4 0.1431
5 0.0231
6 0.0663
3. What is the probability that a resident consumes at most three types of food?
Probability that a resident consumes at most three types of food = (P ≤ 3)
(P ≤ 3) = (P = 1) + (P = 2) + (P = 3)
(P ≤ 3) = 0.4231 + 0.3321 + 0.0123
(P ≤ 3) = 0.7675
Therefore, the probability that a resident consumes at most three types of food = (P ≤ 3)
is 0.7675 (76.75 %)
4. What is the probability that a resident consumes at least four types of food?
Probability that a resident consumes at least four types of food = (P ≥ 4)
(P ≥ 4) = (P = 4) + (P = 5) + (P = 6)
(P ≥ 4) = 0.1431 + 0.0231 + 0.0663
(P ≥ 4) = 0.2325
6. 4
Therefore, the probability that a resident consumes at least four types of food = (P ≥ 4) is
0.2325 (23.25 %)
5. What is expected value/Population mean?
The expected value (EV) is calculated by multiplying each of the possible outcomes by the
likelihood each outcome will occur and then summing all of those values.
EV = ∑ P(Xi) × Xi
EV = (1 × 0.4231) + (2 × 0.3321) + (3 × 0.0123) + (4 × 0.1431) + (5 × 0.0231) + (6 × 0.0663)
EV = 0.4231 + 0.6642 + 0.0369 + 0.5724 + 0.1155 + 0.3978
EV = 2.2099
Therefore, the expected value (population mean) is 2.2099
6. What is the variance of the population around the mean?
σ = √𝑉𝑎𝑟 (𝑋)
σ2 = [(1 - 2.2099)2 0.4231] + [(2 - 2.2099)2 0.3321] + [(3 - 2.2099)2 0.0123] + [(4 - 2.2099)2
0.1431] + [(5 - 2.2099)2 0.0231] + [(6 - 2.2099)2 0.0663]
σ2 = [(-1.2099)2 0.4231] + [(- 0.2099)2 0.3321] + [(0.7901)2 0.0123] + [(1.7901)2 0.1431] +
[(2.7901)2 0.0231] + [(3.7901)2 0.0663]
σ2 = [0.61935832] + [0.0146316651] + [0.0076783735] + [0.4585579412] + [0.1798256] +
[0.9523900861]
σ2 = 2.2324419859 σ = √𝑉𝑎𝑟 (𝑋) σ = √2.2324419859
Therefore, the variance of the population around the mean is 2.23
7. 5
7. In Lami Kura sub-city (Addis Ababa), cases of COVID-19 was reported with a rate of
6.5/day. What is the probability that 2 cases of COVID-19 will be reported in a given day?
(e = 2.71)
Given:
λ = the mean number of occurrences in periods of some interval = 6.5/day
X = the event of the random variable X = 2
e = 2.71
Required:
What is the probability that 2 cases of COVID-19 will be reported in a given day?
Solution:
P(X=x) =
𝑒−λλ 𝑥
𝑋!
P(X=x) =
(𝑒−6.5)6.5 2
2!
= 0.0635203059/2 = 0.031760153
8. Suppose a borderline hypertensive is defined as a person whose DBP is between 80- and
95-mm Hg inclusive, and the subjects are 35-44-year-old males whose BP is normally
distributed with mean 75 and variance 121. What is the probability that a randomly selected
person will be a borderline hypertensive?
Given:
Mean = 75
Variance = 121
DBP is between 80- and 95-mm Hg inclusive.
Required:
What is the probability that a randomly selected person will be a borderline hypertensive?
8. 6
Solution:
Let X be DBP, X ~ N (75, 121)
σ = √𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = √121 = 11
P (80 < 𝑋̅ < 95) = P [
(80 − 75)
11
] < [
(X
̅− µ)
σ
] < [
(95 − 75)
11
]
P (80 < 𝑋̅ < 95) = P [
(80 − 75)
11
] < 𝑍 < [
(95 − 75)
11
]
P (80 < 𝑋̅ < 95) = P (0.45454545454545454545454545454545 < 𝑍 <
1.8181818181818181818181818181818)
Since the Z table shows at two decimal places, I approximated the values to two decimal
places. P (80 < 𝑋̅ < 95) = P (0.46 < 𝑍 < 1.82)
P (80 < 𝑋̅ < 95) = P (0.46 < 𝑍 < 1.82)
P (80 < 𝑋̅ < 95) = P (Z < 1.82) – P (Z < 0.46)
P (80 < 𝑋̅ < 95) = 0.9656 – 0.6772
P (80 < 𝑋̅ < 95) = 0.2884
Thus, approximately 28.84 % of this population will be borderline hypertensive.
9. The mean reading speed of a random sample of 81 adults is 325 words per minute. If the
standard deviation for all adults is 45 words per minute; Find a 90% C.I.
Given:
n = 81
𝑋̅ = 325
σ = 45
90% C.I. = 1.645
Required: Find a 90% C.I.
9. 7
Solution:
𝑋̅ ± Za⁄2 (
σ
√𝑛
)
325±1.645(
45
√81
)= 325±1.645(
45
9
)
325±1.645(5)= 325± 8.225 = (325 - 8.225, 325 + 8.225)
Therefore, the 90% C.I. is (316.775, 333.225)
10.An anthropologist who wanted to study the heights of adult men and women
took a random sample of 128 adult men and 100 adult women which is
normally distributed. Adult men population mean height and SDwere 170cms
and 8cms respectively. Whereas for women 164cms and 6cms respectively.
Find a 95% C.I for the difference of mean height of adult men and women.
Given:
n1 = 128 and n2 = 100
𝑋̅1 = 170 and 𝑋̅2 = 164
σ1 = 8 and σ2 = 6
Required: Find a 95% C.Ifor the difference of mean height ofadult men and women.
Solution:
𝑋̅1 - 𝑋̅2 ± Za⁄2 (√
σ12
𝑛1
+
σ22
𝑛2
) = 170 - 164 ± 1.96(√
82
128
+
62
100
)
10. 8
170 - 164 ± 1.96(√
82
128
+
62
100
)= 6 ± 1.96(√
64
128
+
36
100
) = 6 ± 1.96(√0.5 + 0.36)
170- 164 ± 1.96(√
82
128
+
62
100
)= 6 ± 1.96(√0.86) = 6 ± 1.96(0.927) = 6 ± 1.81692
6 ± 1.81692 = (6 – 1.81692, 6 + 1.81692) = (4.18308, 7.81692)
Therefore, the 95% C.I for the difference of mean height of adult men and women
is (4.18308, 7.81692).