Pre-Cal 40S Slides May 26, 2008
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The document discusses medical testing and probabilities involving events that are independent or mutually exclusive. It provides examples of selecting marbles from a bag, drawing cards from a deck, selecting a class president and treasurer from students, and rolling dice to illustrate independent and dependent events. It also discusses the addition rule for determining the probability of events A or B occurring, or both occurring. Finally, it uses examples to explain calculating the probability that someone testing positive for cancer or industrial disease actually has the condition, given the accuracy of the medical test and prevalence of the disease in the population.
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Use the information below to answer Questions 1 through 4.
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x
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4
4
5
y
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10.
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a) P(survivor was female) = Total females / Total survivors
= 308/450 = 0.685
b) P(survivor was in 1st class) = Total in 1st class / Total survivors
= 193/450 = 0.429
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Use the information below to answer Questions 1 through 4.
Given a sample size of 36, with sample mean 670.3 and sample standard deviation 114.9, we perform the following hypothesis test.
Null Hypothesis
Alternative Hypothesis
1. What is the test statistic?
2. At a 10% significance level (90% confidence level), what is the critical value in this test? Do we reject the null hypothesis?
3. What are the border values between acceptance and rejection of this hypothesis?
4. What is the power of this test if the assumed true mean were 710 instead of 700?.
Questions 5 through 8 involve rolling of dice.
5. Given a fair, six-sided die, what is the probability of rolling the die twice and getting a “1” each time?
6. What is the probability of getting a “1” on the second roll when you get a “1” on the first roll?
7. The House managed to load the die in such a way that the faces “2” and “4” show up twice as frequently as all other faces. Meanwhile, all the other faces still show up with equal frequency. What is the probability of getting a “1” when rolling this loaded die?
8. Write the probability distribution for this loaded die, showing each outcome and its probability. Also plot a histogram to show the probability distribution.
Use the data in the table to answer Questions 9 through 11.
x
3
1
4
4
5
y
1
-2
3
5
9
9. Determine SSxx, SSxy, and SSyy.
10.
Find the equation of the regression line. What is the predicted value when
11. Is the correlation significant at 1% significance level (99% confidence level)? Why or why not?
Use the data below to answer Questions 12 through 14.
A group of students from three universities were asked to pick their favorite college sport to attend of their choice: The results, in number of students, are listed as follows:
Football
Basketball
Soccer
Maryland
60
70
20
Duke
10
75
15
UCLA
35
65
25
Supposed a student is randomly selected from the group mentioned above.
12. What is the probability that the student is from UCLA or chooses football?
13. What is the probability that the student is from Duke, given that the student chooses basketball?
14. What is the probability that the student is from Maryland and chooses soccer?
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16. What is the probability that a randomly selected mango weighs less than 12.5 ounces?
17. A quality inspector randomly selected 100 apples from the shipment.
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- Classical probability which uses equally likely outcomes and sample spaces to calculate probabilities
- Empirical probability which is based on observed frequencies
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- Conditional probability which considers the probability of one event given that another has occurred
Examples are provided to demonstrate calculating probabilities of simple and compound events.
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- Classical probability which uses equally likely outcomes and sample spaces to calculate probabilities
- Empirical probability which is based on observed frequencies
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- Conditional probability which considers the probability of one event given another
- Multiplication rules for independent and dependent events
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- Common reasoning errors like belief bias, availability heuristic, and confirmation bias that can influence judgments.
- Factors that affect inductive arguments like representativeness of observations and number of observations.
- Conditional and categorical syllogisms as forms of deductive reasoning.
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Here are the step-by-step solutions:
a) P(survivor was female) = Total females / Total survivors
= 308/450 = 0.685
b) P(survivor was in 1st class) = Total in 1st class / Total survivors
= 193/450 = 0.429
c) P(survivor was female | survivor was in 1st class) = Females in 1st class / Total in 1st class
= 134/193 = 0.694
d) P(survivor was female and in 1st class) = Females in 1st class / Total survivors
= 134/450 = 0.
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Behind Their Eyes v1
Behind Their Eyes - making thinking visible is not enough
Walk into any classroom and watch the breakneck pace at which teachers are working hard to help students learn. Mind you, if we don’t uncover what students are thinking while learning, they may be running down the wrong path. OK, so we need ways to make student thinking visible. Seeing their thinking is important, but we also need to create the time and space for teachers to absorb, reflect, and act on what their students thinking reveals. This workshop shares strategies both for making student thinking visible and for creating time and space for teachers to meaningfully act on what they learn about what’s going on behind their eyes.
Leading Change v1
“If you really want to understand something, try changing it.” - Kurt Lewin
As the Director of Learning for a school division made up of 18 schools, my job is to help lead the largest change initiative ever undertaken in our school community. One of the most important, difficult, messy things any school leader does is lead change. While we can learn from the change leadership of others, copying their work most often leads to failure. Success is more likely to come from adapting others work to our own context. In this workshop I share the journey we’ve undertaken collectively in our schools; how we developed a shared vision, cultivated collaborative cultures, maintained a focus on deep learning, and wrestle with the nuances of accountability. Informed by the latest research on change management in education, we also model strategies for fostering deep learning conversations in your schools. We’ll engage in some deeper learning conversations together and take back a wealth of ideas you can adapt to your own context. Developing collaborative cultures is careful and precise work that has profound impact when carried out well. So how do you do that? Come, let’s learn together. Good people are important, but good cultures are moreso.
Providing Permission To Wonder v2.1
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore inquiry as a pedagogical stance and the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants will leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
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The document is a presentation about digital citizenship given by Darren Kuropatwa at the Building Learning Communities Conference in Boston, MA in July 2017. It discusses the importance of digital citizenship and responding to adversity with persistent kindness. It provides examples of digital citizenship issues and scenarios for discussion. It encourages participants to think about their own digital footprint and how to be good digital citizens.
Digital Storytelling for Deeper Learning v1
Presented at the Riding the Wave Conference in Gimli, Manitoba. May 2017.
In two words, you remember the whole story: glass slipper, sour grapes, cold porridge. You remember more than facts, you recall relationships & deeper connections between characters. Some of the powerful ways we leverage digital for deeper learning includes challenging sources of information (fake news), exploring bias (developing empathy through multiple perspectives), and creating powerful feedback loops that foster deeper learning.
Powerful narratives, in a word or two, bring to mind a wealth of ideas & relationships; more than just facts. How can we find stories that make our teaching sticky and help kids find, and more importantly tell, stories that make learning stick? This workshop will equip teachers with the skills & knowledge to foster deeper learning across the curriculum by intentionally leveraging digital tools to foster deeper learning.
Tales of Learning and the Gifts of Footprints v4.2
This document appears to be a presentation about digital learning and storytelling. It discusses shifting from compliance to care, private to public learning, and consumer to participatory models. It addresses what digital storytellers look like and principles of learning including starting where students are, learning being done by and for students, students talking about learning, having learning targets, and feedback. It encourages generosity, sharing tales of learning, and giving the gifts of footprints.
The Fourth Screen v4.2
Presented at the Richmond District Conference, Feb 2017.
A series of stories woven together to start a conversation with middle and high school students, teachers, and parents about living our lives on and offline (on The Fourth Screen) more thoughtfully.
This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
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Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning. Held at the BYTE Conference 2017 in Portage la Prairie, Manitoba.
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A group of educators from the BYTE Conference 2017 (Build Your Teaching Experience) share their ideas about learning as a series of visual metaphors they found on their phones.
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The document discusses storytelling and how it can be used as a tool for learning. It suggests that storytelling allows students to think in metaphors and learn through stories. It provides examples of how digital tools like QR codes and apps can be used to incorporate storytelling into the classroom. It also outlines some rules of thumb for using storytelling, such as personalizing tasks to students' experiences, collaborating on group projects, and getting feedback from both inside and outside the classroom.
Providing Permission to Wonder v3
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
The Fourth Screen v4.1
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Providing Permission to Wonder v2
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
The Fourth Screen v4
This document contains a collection of images, quotes, and short passages on topics related to online communities, sharing, and empowerment through technology. The snippets discuss how the internet allows information to be easily shared, encourages learning, and can help empower victims of bullying. The overarching theme is about the positive impact community and connection through online platforms can provide.
Learning is at BLC16
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Slides to support a master class at the Building Learning Communities Conference in Boston, MA. 18 July 2016.
How can we make learning sticky using powerful storytelling frameworks that tap into peoples' emotions? How do we involve all students in creating digital content that doesn't also create hours of content for teachers to assess? This interactive session will showcase Digital Storytelling activities teachers can use in class tomorrow! Document student learning & foster reflective ways for students to share their learning. 1st: we play! Then we'll discuss how to practically adapt these ideas, make them your own, and figure out what sort of infrastructure needs to be in place to support these kinds of powerful learning experiences. We’ll learn how to exercise your students' & your own creativity muscles and share simple strategies for collecting & publishing student work.
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Pharmacological actions-
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4) Anticholinergic action- many H1 blockers
in addition antagonize muscarinic actions of ACh. BUT IN 2ND gen histaminics there is Higher H1 selectivitiy : no anticholinergic side effects
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Gastrointestinal Infections
GASTROINTESTINAL INFECTIONS result from the ingestion of pathogens that cause infections at the level of this tract, generally being transmitted by food, water and hands contaminated by microorganisms such as E. coli, Salmonella, Shigella, Vibrio cholerae, Campylobacter, Staphylococcus, Rotavirus among others that are generally contained in feces, thus configuring a FECAL-ORAL type of transmission.
Among the factors that lead to the occurrence of gastrointestinal infections are the hygienic and sanitary deficiencies that characterize our markets and other places where raw or cooked food is sold, poor environmental sanitation in communities, deficiencies in water treatment (or in the process of its plumbing), risky hygienic-sanitary habits (not washing hands after major and/or minor needs), among others.
These are generally consequences (signs and symptoms) resulting from gastrointestinal infections: diarrhea, vomiting, fever and malaise, among others.
The treatment consists of replacing lost liquids and electrolytes (drinking drinking water and other recommended liquids, including consumption of juicy fruits such as papayas, apples, pears, among others that contain water in their composition).
To prevent this, it is necessary to promote health education, improve the hygienic-sanitary conditions of markets and communities in general as a way of promoting, preserving and prolonging PUBLIC HEALTH.
Gastritis and Gastric Health
Gastric Health is one of the most relevant concerns in human health, with gastrointestinal infections being among the main illnesses that affect humans.
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In addition to bacterial infections, gastritis and gastric ulcers are associated with several factors, with emphasis on prolonged fasting, chemical substances including drugs, alcohol, foods with strong seasonings including chilli, which ends up causing inflammation of the stomach walls and/or corrosion. of the same, resulting in the appearance of wounds and consequent gastritis or ulcers, respectively.
Among patients with gastritis and/or ulcers, one of the dilemmas is associated with the foods to consume in order to minimize the sensation of pain and discomfort. Hemodialysis: Chapter 6, Hemodialysis Adequacy and Dose - Dr.Gawad
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Breast cancer in postmenopausal women with hormone receptor-positive (HR+) status is a common and complex condition that necessitates a multifaceted approach to management. HR+ breast cancer means that the cancer cells grow in response to hormones such as estrogen and progesterone. This subtype is prevalent among postmenopausal women and typically exhibits a more indolent course compared to other forms of breast cancer, which allows for a variety of treatment options.
Diagnosis and Staging
The diagnosis of HR+ breast cancer begins with clinical evaluation, imaging, and biopsy. Imaging modalities such as mammography, ultrasound, and MRI help in assessing the extent of the disease. Histopathological examination and immunohistochemical staining of the biopsy sample confirm the diagnosis and hormone receptor status by identifying the presence of estrogen receptors (ER) and progesterone receptors (PR) on the tumor cells.
Staging involves determining the size of the tumor (T), the involvement of regional lymph nodes (N), and the presence of distant metastasis (M). The American Joint Committee on Cancer (AJCC) staging system is commonly used. Accurate staging is critical as it guides treatment decisions.
Treatment Options
Endocrine Therapy
Endocrine therapy is the cornerstone of treatment for HR+ breast cancer in postmenopausal women. The primary goal is to reduce the levels of estrogen or block its effects on cancer cells. Commonly used agents include:
Selective Estrogen Receptor Modulators (SERMs): Tamoxifen is a SERM that binds to estrogen receptors, blocking estrogen from stimulating breast cancer cells. It is effective but may have side effects such as increased risk of endometrial cancer and thromboembolic events.
Aromatase Inhibitors (AIs): These drugs, including anastrozole, letrozole, and exemestane, lower estrogen levels by inhibiting the aromatase enzyme, which converts androgens to estrogen in peripheral tissues. AIs are generally preferred in postmenopausal women due to their efficacy and safety profile compared to tamoxifen.
Selective Estrogen Receptor Downregulators (SERDs): Fulvestrant is a SERD that degrades estrogen receptors and is used in cases where resistance to other endocrine therapies develops.
Combination Therapies
Combining endocrine therapy with other treatments enhances efficacy. Examples include:
Endocrine Therapy with CDK4/6 Inhibitors: Palbociclib, ribociclib, and abemaciclib are CDK4/6 inhibitors that, when combined with endocrine therapy, significantly improve progression-free survival in advanced HR+ breast cancer.
Endocrine Therapy with mTOR Inhibitors: Everolimus, an mTOR inhibitor, can be added to endocrine therapy for patients who have developed resistance to aromatase inhibitors.
Chemotherapy
Chemotherapy is generally reserved for patients with high-risk features, such as large tumor size, high-grade histology, or extensive lymph node involvement. Regimens often include anthracyclines and taxanes.
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The Children are very vulnerable to get affected with respiratory disease.
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1. **Epidermis**: The outermost layer primarily composed of epithelial cells called keratinocytes. It provides a protective barrier against environmental factors, pathogens, and UV radiation.
2. **Dermis**: Located beneath the epidermis, the dermis contains connective tissue, blood vessels, hair follicles, and sweat glands. It plays a vital role in supporting and nourishing the epidermis, regulating body temperature, and housing sensory receptors for touch, pressure, temperature, and pain.
3. **Hypodermis**: Also known as the subcutaneous layer, it consists of fat and connective tissue that anchors the skin to underlying structures like muscles and bones. It provides insulation, cushioning, and energy storage.
Skin performs essential functions such as regulating body temperature through sweat production and blood flow control, synthesizing vitamin D when exposed to sunlight, and serving as a sensory interface with the external environment.
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Pre-Cal 40S Slides May 26, 2008
- 1. Medical Testing or Why are doctors so darn cagey?!? Let me check your sugar. by flickr user Cataract eye
- 2. Identify the events as: dependent mutually exclusive Drag'n Drop Baby! independent not mutually exclusive a. A bag contains four red and seven black marbles. The event is randomly selecting a red marble from the bag, returning it to the bag, and then randomly selecting another red marble from the bag. independent mutually exclusive b. One card - a red card or a king - is randomly drawn from a deck of cards. independent not mutually exclusive c. A class president and a class treasurer are randomly selected from a group of 16 students. dependent mutually exclusive d. One card - a red king or a black queen - is randomly drawn from a deck of cards. mutually exclusive independent e. Rolling two dice and getting an even sum or a double. independent not mutually exclusive
- 4. Testing for independence ... 30% of seniors get the flu every year. 50% of seniors get a flu shot annually. 10% of seniors who get the flu shot also get the flu. Are getting a flu shot and getting the flu independent events?
- 5. Probabilities involving quot;andquot; and quot;orquot; A.K.A quot;The Addition Rulequot;... The addition rule is a result used to determine the probability that event A or event B occurs or both occur. The result is often written as follows, using set notation: P(A or B) = P(A B) = P(A)+P(B) - P(A B) where: P(A) = probability that event A occurs P(B) = probability that event B occurs P(A U B) = probability that event A or event B occurs P(A B) = probability that event A and event B both occur P(A and B) = P(A B) = P(A)*P(B)
- 6. Suppose a test for cancer is known to be 98% accurate. This means that the outcome of the test is correct 98% of the time. Suppose that 0.5% of the population have cancer. What is the probability that a person who tests positive for cancer has cancer? Suppose 1 000 000 randomly selected people are tested. There are four possibilities: • A person with cancer tests positive • A person with cancer tests negative • A person without cancer tests positive • A person without cancer tests negative
- 7. Suppose a test for cancer is known to be 98% accurate. This means that the outcome of the test is correct 98% of the time. Suppose that 0.5% of the population have cancer. What is the probability that a person who tests positive for cancer has cancer? (1) (a)How many of the people tested have cancer? (b) How many do not have cancer? (2) Assume the test is 98% accurate when the result is positive. (a) How many people with cancer will test positive? (b) How many people with cancer will test negative? (3) Assume the test is 98% accurate when the result is negative. (a) How many people without cancer will test positive? (b) How many people without cancer will test negative? (4) (a) How many people tested positive for cancer? (b) How many of these people have cancer? (c) What is the probability that a person who tests positive for cancer has cancer?
- 8. Suppose a test for cancer is known to be 98% accurate. This means that the outcome of the test is correct 98% of the time. Suppose that 0.5% of the population have cancer. What is the probability that a person who tests positive for cancer has cancer?
- 9. Suppose a test for cancer is known to be 98% accurate. This means that the outcome of the test is correct 98% of the time. Suppose that 0.5% of the population have cancer. What is the probability that a person who tests positive for cancer has cancer?
- 10. Suppose a test for industrial disease is known to be 99% accurate. This means that the outcome of the test is correct 99% of the time. Suppose that 1% of the population has industrial disease. What is the probability that a person who tests positive has industrial disease?