# Maths

## Binomial Experiments

What are the key characteristics of a binomial probability distribution? Explain whether the following two experiments have all these characteristics. Determine if they binomial experiments or not. (a) Flipping a coin, let x be the number of tosses needed to get ahead for the first time. (b) Rolling a die 10 times, let x be the number of 6 shown. Use formal writing to answer these questions. For more information on this check: https://en.wikipedia.org/wiki/Binomial_distribution

## Data Collection and Analysis

Final Project and Presentation details: Students will perform data collection and analysis on a topic of their choice, with the goal of establishing a linear correlation. Often times this portion of the project is more art than science since many experiments do not turn out a linear dependence. Students must submit a project summary by July 31st, 2020 so that the instructor may modify it or make suggestions. The data should be collected, along with statistical errors on the measurements. Students will then perform a linear regression on the data, and attempt to make a sound statistical prediction using the regression. The final presentation should be 7-12 slides in PDF or PowerPoint format, which will be presented remotely to the class via Zoom in the final week of class. In addition to the technical correctness of the conclusions, students will be assessed on the clarity of the presentation. As such, the instructor will provide practice sessions, training, and advice on the presentation of the topic by appointment with the students.

## Fraction Concepts

You are working with a middle school class that loses focus easily and over half of the students struggle with fraction concepts. Design a bridging activity linking addition and subtraction of fractions to an abstract, pencil and paper assignment. Be sure to explain the teaching sequence carefully as if leaving exact notes for a substitute teacher who has never seen or used the activities before. Include some scripting as well. I will attach the chapter notes i have taken, please review them carefully and use appropriate terminology and procedures outlined in the notes.

## Probability Distribution

Select a discrete probability distribution and present a real-life application of that distribution. Interpret the expected value and the standard deviation of your selected distribution within the context of the real-life example that you have selected, and describe how these values can be used by enterprise decision-makers. Select a continuous probability distribution and present a real-life application of that distribution. Interpret the expected value and the standard deviation of your selected distribution within the context of the real-life example that you have selected, and describe how these values can be used by enterprise decision-makers.

## Measures of Central Tendency and Variability

Understanding descriptive statistics, their measures of center and their variability helps form the foundation of statistical analysis. Descriptive statistics tell us how frequently an observation occurs, what is considered average, and how far data in our sample deviate from being average. With these statistics, we are able to provide a summary of characteristics from both large and small datasets. Measures of central tendency and variability provide valuable information on their own and form the cornerstone of the quantitative structures that we build in our research studies. Required Resources Read/review the following resources for this activity: OpenStax Textbook: Chapter 2 Lesson Minimum of 1 scholarly source In your reference for this assignment, be sure to include both your text/class materials AND your outside reading(s). Initial Post Instructions For this Discussion, you will examine the central tendency and variability in terms of pulse rate. Find and record the pulse rate of 10 different people where you work. Tell us a little about the population from which you drew your data. Describe your findings in terms of central tendency and variability. Consider using some of the following to help you form your initial discussion post: What are your measures of central tendency (i.e., mean, median, and mode)? Which might be the better measure for central tendency and why? What is the standard deviation of your data? How variable are the data (range)? Are there any outliers? Investigate possible reasons for these outliers, and things that might limit them if the further study were to be carried out. What are some variables that should be considered in discussing your measures of central tendency and variation? Is there any skewness in your measured data? How would you describe this data (i.e. what insights did you gain from this data)?

## Newton’s Raphson Method

Description: Newton’s Raphson Method 2-Langrange Interpolation polynomial 3-Newton Divided Difference 4- Numerical differentiations 5-Numerical integration 6- Composite Numerical integration. And their 2 applications

## Hypothesis Test

For this assignment, please watch the following video (copy and paste if the link doesn’t work): https://nutritionfacts.org/how-not-to-diet/ (Links to an external site.) Evidence-based is key, not hearsay nor anecdotal evidence does it but statistics! 🙂 This is evidence-based methods for losing weight, losing fat. This will always be good to know for everyone. So you are welcome. Watch the video as much as you like but see at least two hypothesis tests with p-values, (like p < .001) and at least two confidence intervals and at least two graphs. You will probably want to watch the whole thing. Watch at least the first 20 minutes of it. Then please comment on impressed you and what you would want to tell others. State a hypothesis test with a p-value and a confidence interval and state what they both meant and what they show. This will also show that you actually watched it which is necessary to show for this assignment. It will be graded on 4 points for a confidence interval and what it meant, 4 points on stating a hypotheses test with a p-value and what it means, and 1 point each for responding to others. Minus one point as always if it's done lately.

## Trigonometry

Determine the solutions in the interval [?2?, 2?] to the following trigonometric equation. You may leave one of your solutions in the exact form x = arccos y. You must show all of your steps. Mysterious or unsupported work will not be counted. 1 + cos2 x = 2 sin x 2.

## Graphing and Describing Data

For the first set of data, a list of all the injuries seen in a clinic over a month, I would use a frequency table and include the relative frequency. Relative frequency would be the ratio of the number of each injury to the number of total injuries seen in the clinic. This would give a good idea in percentage form of how often the clinic is seeing each type of injury. I would choose to display this data in a pie chart. A pie chart is visually easy to read and is good for qualitative data and relative frequencies (Chamberlain College, n.d.). The size of each slice of pie is proportional to the data value in each category (Williams & Anderson, 2020). By using a pie chart for this data, it would be easy to quickly look and see which injuries the clinic is seeing the most of, and which injuries are less commonly being seen. For the second set of data, the number of minutes that each patient spends in the waiting room of the doctors office, I would use a cumulative frequency table. The cumulative frequency uses each relative frequency and adds it to the next, making it cumulative. I would use this method to organize the data because then I could look and see what percentage of patients are waiting a certain amount of time or less. For example, if the relative frequency of patients waiting 10 minutes is 0.25 and the relative frequency of patients waiting 20 minutes is 0.6, then that means that the cumulative frequency is 0.85. This indicates that 85% of patients are waiting 20 minutes or less to be seen by the doctor. I would choose to display this data with a stem and leaf plot. This is a good choice when you have a smaller number of data points (Holmes, Illowsky, & Dean, 2017). The stem would include the tens, and the leaf would include the ones. Because a doctors office probably doesnt see a very large number of patients in a day, this would be a good option to easily display this data in minutes waited. Marissa Whitmore References: Chamberlain College of Nursing. (n.d.). Week 2 lesson: Graphing and describing data. https://chamberlain.instructure.com/courses/65726/pages/week-2-lesson-graphing-and-describing-data?module_item_id=8751247 Holmes, A., Illowsky, B., & Dean, S. (2017). Introductory business statistics. OpenStax. https://openstax.org/details/books/introductory-business-statistics (Links to an external site.) Williams, T., & Anderson, D. (2020, February 03). Statistics. Retrieved July 13, 2020, from https://www.britannica.com/science/statistics

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