Probability plays a major role in the medical community. Diagnoses are based on probabilities. They are really questions or “what if’s”, and are answered by the probability that the treatment will be the best for the ailment.

Let’s look at probability in terms of both the real world and the medical community.

1. Survey 30 people to find out if they are left-handed or right-handed, and use the following chart to create a contingency table with the information.

Left handed Right handed Total Female Male Total

1. Answer the following questions about the information in your contingency table:
   1. If a person is randomly selected from the survey participants, what is the probability that the person will be left-handed?
   2. If you randomly choose a female from the people you surveyed, what is the probability that she is left-handed?
   3. What is the odds ratio of choosing a left-handed female?
   4. What is the relative risk of choosing a left-handed female?

Example

	Green	Blue	Total
Cats	40 (A)	20 (B)	60 (A+B)
Dogs	30 (C)	40 (D)	70 (C+D)
Total	70 (A+C)	60 (B+D)	130 (A+B+C+D)

1. Probability of Green – (A+C)/(A+B+C+D): 70/130 = 0.54
2. Probability of Green Cat – A/(A+B): 40/60 = 0.67
3. Odds Ratio of Green Cat – (A/B)/(C/D) or AD/BC: (4040)/(2030) = 1600/600 = 2.67
4. Relative Risk of Green Cat – [A/(A+C)]/[B/(B+D)]: (40/70)/(20/60) = 1.71

1. Skim through at least one of the following articles on left-handed vs. right-handed people from the Chamberlain Library. Answer the following question: How do the probabilities and percentages for your study compare to those in the study you read?
   1. https://search-proquest-com.chamberlainuniversity.idm.oclc.org/nahs/docview/211689160/DB2AB8D1E63B4638PQ/4?accountid=147674 (Links to an external site.)
   2. https://search-proquest-com.chamberlainuniversity.idm.oclc.org/nahs/docview/1326739712/DB2AB8D1E63B4638PQ/10?accountid=147674

Can you help me understand this Differential Equations question?

Please solve this partial differential equation using Laplace transforms. Answer with complete solution and explanation. Need it in 6 hours. Thanks!

Hypothesis Testing – Test of Independence

1. You would like to see if the output (minor defect, major defect and good) is independent of the Shift. Construct a hypothesis test, complete the expected and chi square tables as well as answering the questions asked of the discussion board. Use a level of significance of .05.
I included a picture of the full question.

I need help with a Geometry question. All explanations and answers will be used to help me learn.

Find the locus of the center of sphere of constant radius which passes through a given point and touches the given line.

Assessment 3 Instructions: Analyzing Data With Descriptive Statistics

• PRINT
• Use a data generator to produce data for the questions you developed in the previous assessment.
  

  Introduction

  Note: Complete Assessment 2 before completing this assessment .In this assessment, you will use a data generator to produce data for your previously developed questions. You will then summarize the data by calculating various descriptive statistics and present the results graphically.

  Demonstration of Proficiency

  By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies through the following assessment scoring guide criteria.

  • Competency 1: Interpret a data set’s central tendency and variability using descriptive statistical procedures.
    • Calculate proportions correctly.
    • Calculate means correctly.
    • Calculate medians correctly.
    • Calculate modes correctly.
    • Calculate standard deviations correctly.
    • Calculate ranges correctly.
  • Competency 4: Solve problems in your personal and professional life by applying statistical procedures.
    • Explain interesting findings or comparisons as a table, graph, or chart.

  Note: Complete Assessment 2 before completing this assessment.The following resources are required to complete Assessment 3. For this assessment, it very important that you have a good grasp on using Excel for numerical calculations and graphing. Review the resources as needed before attempting Assessment 3.

  Data Generator Link

  Use the Survey Data Generator, which will provide you with simulated data for the questions you specified in Assessment 2. Enter the minimum value, maximum value, and expected value/typical response value you specified for the quantitative questions (Q5 and Q6) in Assessment 2. Then, click “Download Excel Spreadsheet.” The Excel file will be saved in the download folder of your computer.Note: You might receive an alert about the file extension of the downloaded Survey Data Generator file. Click “Yes” to open the file.

  Software

  Capella University requires learners to meet certain minimum computer requirements. As a Capella learner, to purchase some required or recommended software at a substantially reduced price, visit the Capella Software Store. Some software required for a course may exceed these requirements, in which case it will be provided to you via a virtual desktop or as part of your course materials. The following software is required to complete learning activities in this assessment.

  • Microsoft Excel: Version 2010 or newer.
    • Windows PC users: The Analysis Toolpak in Excel is a free add-in program—it provides data analysis tools that allow you to complete more complex statistical functions. If you do not yet have the add-in available in Excel, see instructions in Microsoft’s Loading the Analysis Toolpak in Excel.
    • Mac users: MS Excel 2016 has an available Toolpak add-in. For all other Mac users: StatPlus: mac LE is the free equivalent for Apple users, but must be downloaded from AnalystSoft.

  Microsoft Office/Excel Resources

  • Microsoft Corporation. (n.d.). Office support. Retrieved from http://office.microsoft.com/en-us/support
    • Loading the Analysis Toolpak in Excel. Retrieved from https://support.office.com/en-us/article/Load-the-…
  • AnalystSoft. (n.d.). StatPlus: mac LE. Retrieved from https://www.analystsoft.com/en/products/statplusma…

  After having defined your survey questions in Assessment 2, you are now able to produce data. This will be done by using a data generator tool that generates hypothetical data for the questions you developed in Assessment 2. The data generator gives you information similar to what you might get when conducting the survey with actual persons.Once you have obtained the data by using the generator tool, use Excel to conduct your analysis and interpret the data using descriptive statistics and visual representations of the data.

  Data Generation and Preparation

  Step 1: Generate Data Using the Survey Data Generator.

  • Open the Survey Data Generator. The Survey Data Generator will generate responses to the set of six survey questions you previously defined. It knows nothing about the particular subject of your study; it only generates a set of responses to question types that are pre-defined.
  • Type the minimum, the maximum, and the expected values for questions 5 and 6 into the Survey Data Generator. (These are values for the quantitative questions from Table 1 of your completed Data Collection Template.) Note that the generator has spaces only for the values for your two quantitative questions.
    • For the top set of boxes, enter the values for question 5.
    • For the bottom set of boxes, enter the values for question 6.
    • You must enter a single number for the minimum, the maximum, and the expected value for each of these questions.
    • Do not enter any commas, decimal points, or other symbols.
  • You will not enter anything into the generator for your binary questions (1–4). The tool knows that the only possible responses for these questions are 0 and 1. It will automatically generate 0s and 1s for the responses to your binary questions. Assign 0 and 1 to the two possible responses; it is up to you which response to assign 0 and which to assign 1. For example, if you asked “Are you male of female?” you could make Male = 0 and Female = 1, or vice versa.
  • The Survey Data Generator will create an Excel file that represents responses to your questions. Once you have your unique survey data in Excel, you can apply descriptive statistics to the data and present your results in different visual representations to help an audience easily scan and understand your results.
  • Explanation of data in Excel:
    • There will be six columns (A–F) in Excel: one column for each question (1–6).
    • Columns A–D represent the responses for questions 1–4 and should only contain 0s and 1s. Columns E and F represent the responses for questions 5–6 and should contain numbers between your minimum and maximum.
    • Each row will represent the responses from one survey participant. For example, the first row of answers represents the first survey participant’s answers to all six questions. The second row of answers represents the second survey participant’s answers to the questions, and so forth. The number of rows of answers is how many participants completed the survey.
    • If a column contains all the same numbers, you need to use the Survey Data Generator again. There has to be variation in these responses for you to statistically analyze the data. Check to see that columns 1 through 4 contain a mix of 0s and 1s and that columns 5 and 6 contain a range of different numbers between your minimum and maximum.

  Step 2: Prepare for Data Analysis in Excel.

  • To be able to create a histogram in Excel, you need to be able to access the Data Analysis command. It should be visible on the Data tab, in the Analysis group to the far right in Excel. If it is not visible, you will need to install the Analysis ToolPak add-in.
    • For instructions on loading the Analysis ToolPak add-in as well as for creating histograms, which is one of your tasks in this assessment, follow the steps on the Microsoft Microsoft Office Support site. Mac users: StatPlus: mac LE is the free equivalent for Apple users, but must be downloaded from AnalystSoft. Note: MS Excel 2016 now has an available Toolpak add-in. For more information, see the Software section under Required Resources.
    • Enter the word “histogram” into the search box, and you will find information on how to install the ToolPak for your version of Excel as well as information on histograms.
  • If you are not familiar with using Excel and its functions, a variety of helpful resources are provided in the Resources. In addition, you can choose any of the Excel tutorials from the Supplemental Resources in the left navigation menu of your courseroom.
  • Technology note: You will need to sort or rearrange your data to accomplish some of these tasks. Be sure you keep a copy of your original Excel file as a backup.
  • Results note: Because the survey data generation is done without context, you will have to put aside any preconceived notions about how your data should look. Your task is to analyze, interpret, and communicate the unique results.

  Data Analysis and Interpretation

  Complete your analysis (Parts 1–3) on one Excel sheet. Include the following components in your analysis of the data. You may wish to refer to the Analyzing Data With Descriptive Statistics Example [PDF] for further explanation. Note that in order to cover all the survey questions, your submission should include more tables, graphs, and charts than you see in the example.

  Part 1: Questions 1, 2, 3, and 4 (Binary Questions)

  Each question 1–4 should have the following elements:

  • Sample size.
  • Sample proportion of each response.
  • Bar chart or pie chart.

  Part 2: Questions 5 and 6 (Quantitative Questions)

  Questions 5 and 6 should have the following elements:

  • Sample mean.
  • Sample median.
  • Sample mode.
  • Sample range.
  • Sample standard deviation.
  • Sample minimum and maximum.
  • Histogram.

  Part 3: Exploration of Data

  Next, explore your data a bit further. What are two interesting findings from your survey responses? You might investigate responses for selected variables based on responses to your binomial questions. For example, if the answer to question 1 was Male or Female and to question 6 was Annual Income, you might examine average annual income for males only and females only and compare these results. Present your findings in an appropriate table, graph, or chart. Then write, in the same Excel spreadsheet, a 1–2 paragraph summary of your findings.

  Assessment Submission Instructions

  Submit your Excel spreadsheet containing Parts 1–3. Before submitting your assessment, verify you have included all of the elements listed above for Parts 1–3. It is important to note that you should have:

  • Four bar graphs (or four pie charts), one each for questions 1–4.
  • Two histograms, one each for questions 5 and 6.
  • Two tables, graphs, or charts to represent interesting findings from your survey responses. Include a 1–2 paragraph summary of your findings.

Assignment 1b: Representing Addition and Subtraction Word Problems

Submission Instructions: Write your answers to the problems on paper and then scan or take photos of those pages. If there are multiple pages to your completed assignment, you must submit them as one multi-page document (pdf, docx, jpg, or png).

Directions: Complete each of the following. Label the strip diagram using words (e.g., pears) and numbers (e.g., 49) so that anyone can easily interpret your diagram. Put a question mark in the strip diagram to indicate the unknown quantity.

1. Maria picked 15 apples and 22 pears. How many more pears than apples did she pick?
   1. Draw a strip diagram to represent the relationship between the quantities.
   2. How many more pears than apples did Maria pick?
2. The San Diego Zoo has 8 more gorillas than the Bronx Zoo. The San Diego Zoo has 14 gorillas. How many gorillas does the Bronx Zoo have?
   1. Draw a strip diagram to represent the relationship between the quantities.
   2. How many gorillas does the Bronx Zoo have?
3. Tomika baked some cookies. After donating 36 of them to a bake sale, she still had 10 cookies. How many cookies did she bake?
   1. Draw a strip diagram to represent the relationship between the quantities.
   2. How many cookies did Tomika bake?
4. There were only 40 cans of soup on the grocery shelf. Maria restocked the soup, bringing the total up to 200 cans. How many cans did Maria add to the shelf?
   1. Draw a strip diagram to represent the relationship between the quantities.
   2. How many cans did Maria add to the shelf?
5. A party room was decorated with 34 balloons. How many were left after 11 of them broke?
   1. Draw a strip diagram to represent the relationship between the quantities.
   2. How many balloons remained?

1. Find the Y intercept and the slope of the line 3x – 2Y = 12a.

The Y intercept is -6 and the slope is + 3/2b.

The Y intercept is 2 and the slope is – 3/2c.

The Y intercept is 2 and the slope is 3/2d.

The Y intercept is -6 and the slope is + 2/3

2. What is the slope of a line that passes through (2, – 3) and (5, 1)?
a.-4/5b.5/4
c.-3/2d.4/3

3. It costs $2,700 to manufacture 100 items of a product, and $4,200 to manufacture 200 items. If x represents the number of items, and Y the costs, find the cost equation.a.

The (X, Y) coordinates are (100, 2700) and (200, 4200) and the cost function is Y = 1,200 – 15Xb.

The (X, Y) coordinates are (2700, 100) and (200, 4200) and the cost function is Y = 1,200 + 15Xc.

The (X, Y) coordinates are (100, 2700) and (200, 4200) and the cost function is Y = 1,200 + 15Xd.

The (X, Y) coordinates are (100, 2700) and (4200, 200) and the cost function is Y = 1,200 – 15X

4. It costs $2,700 to manufacture 100 items of a product, and $4,200 to manufacture 200 items. If x represents the number of items, and Y the costs, find the cost equation and use this function to predict the cost of 1,000 items.
a.The unit cost of production is $27 + $42 = $69

b.The variable cost of production per unit is $15

c.The unit cost of production $42

d.The unit cost of production is $27.00

Section 2.2: 1, 10

Section 2.3: 4

Section 2.4: 2

Section 2.5: 3

Section 2.7: 6

Exercise A

Write the following dierential equations as a rst order autonomous ODE system:

(a) x sin(x_ ) + x = 0

(b) x + t

p

1 + x2 = 3

Exercise B

For r; x0; v0 2 R nd the explicit solutions x(t) of the following dierential equations:

(a) x_ = rx, x(0) = x0,

(b) x_ = rx2, x(0) = x0,

(c) x_ = rx3, x(0) = x0,

(d) x + x_ 2x = 0, x(0) = x0 and x_ (0) = v0:

Analyze the following equations graphically. In each case, sketch the vector field

on the real line, find all the fixed points, classify their stability, and sketch the

graph of x ( t ) for different initial conditions. Then try for a few minutes to obtain

the analytical solution for x ( t ); if you get stuck, don’t try for too long since in several

cases it’s impossible to solve the equation in closed form!

2.2.1 x = 4×2 −16

2.2.10 (Fixed points) For each of (a)–(e), find an equation x f (x) with the

stated properties, or if there are no examples, explain why not. (In all cases, assume

that f ( x ) is a smooth function.)

a) Every real number is a fixed point.

b) Every integer is a fixed point, and there are no others.

c) There are precisely three fixed points, and all of them are stable.

d) There are no fixed points.

e) There are precisely 100 fixed points.

2.3.4 (The Allee effect) For certain species of organisms, the effective growth

rate N N is highest at intermediate N. This is called the Allee effect (Edelstein–

Keshet 1988). For example, imagine that it is too hard to find mates when N is very

small, and there is too much competition for food and other resources when N is

large.

a) Show that N N = r−a(N −b)2 provides an example of the Allee effect, if r, a,

and b satisfy certain constraints, to be determined.

b) Find all the fixed points of the system and classify their stability.

c) Sketch the solutions N ( t ) for different initial conditions.

d) Compare the solutions N ( t ) to those found for the logistic equation. What are

the qualitative differences, if any?

Use linear stability analysis to classify the fixed points of the following systems.

If linear stability analysis fails because f ′(x∗) 0, use a graphical argument to

decide the stability.

2.4.2 x = x(1−x)(2−x)

2.5.3 Consider the equation x = rx+x3 , where r 0 is fixed. Show that x ( t )

in finite time, starting from any initial condition x0 0.

For each of the following vector fields, plot the potential function V ( x ) and identify

all the equilibrium points and their stability.

2.7.6 x = r+x−x3 , for various values of r.

Exercise A

Write the following dierential equations as a rst order autonomous ODE system:

(a) x .. sin(x_ ) + x = 0

(b) x + t

p

1 + x2 = 3

Exercise B

For r; x0; v0 2 R nd the explicit solutions x(t) of the following dierential equations:

(a) x_ = rx, x(0) = x0,

(b) x_ = rx2, x(0) = x0,

(c) x_ = rx3, x(0) = x0,

(d) x + x_ .. 2x = 0, x(0) = x0 and x_ (0) = v0:

I don’t understand this Statistics question and need help to study.

Consider a situation that you might want to study through a statistical lens. The situation would require you to study a small sample and make an inference to the population. For example, you might want to understand how likely children are to complete their homework when considering their individual characteristics or maybe you want to understand if children who eat broccoli are more likely to complete their homework than those who do not.

• How would you select a test that was appropriate to answer your question?
• How would you rule out tests that were not appropriate to answer your question?