Mathematics

HW #5 Z-scores A normal distribution of scores has a standard deviation of ? =10; and a ? = 70. Find the z-scores corresponding to each of the following values: a) A score that is 20 points above the mean. (Hint: what score is 20 points above the mean of ? = 70?) b) A score that is 10 points below the mean. c) A score of x = 50. d) A score of x = 35.

The most commonly used descriptive statistics are measures of central tendency including mean, median, and mode. In this assignment, you will watch some informative videos to become familiar with SPSS, enter data, and then answer some basic questions about a data set. General Requirements: Use the following information to ensure successful completion of the assignment: Review “SPSS Access Instructions” for information on how to access SPSS for this assignment. Doctoral learners are required to use APA style for their writing assignments. The APA Style Guide is located in the Student Success Center. You are not required to submit this assignment to LopesWrite. Directions: View the following: SPSS for Beginners 1 – Introduction SPSS for Beginners 2a: Frequency Counts SPSS for Beginners 2b: Descriptive Statistics and Z-scores Graphing and Descriptive Stats in SPSS With Dr. Ami Gates Open SPSS and complete the following: Obtain an output (as in the tutorials), highlight the selected statistical values for each gender as listed below, and upload it into LoudCloud. Determine the statistics for each gender as follows: Frequency Counts, Mean, Standard Deviation, Minimum, and Maximum Create a bar graph with gender (axis X) and height (axis Y). Upload the output into LC. Data Set: Male: 74, 71, 75, 62 Female: 62, 68, 61, 71, 68, 80

Using the information in the master budget and cash budget attached how can this be used by the managers of garden furnishing ltd to improve the financial performance and the situation of the organisation. Please consider the following issues that have arose within the organisation Revenues and selling prices are on a similar level to competitors but business has much higher costs than competitors do, which seems to be leading to smaller profit margins than its direct competitors are. The business is also very seasonal (high sales in spring and summer) therefore; the lack of budgeting has regularly left the business in very bad cash flow situations. Garden Furnishings Ltd is a manufacturing business that produces garden furniture for the retail market. It is a family owned business that has historically had a relaxed approach to budgeting and business in general with a reluctance to change. The business is seasonal and although selling prices are comparable to those of their competitors, the profit margins are low. Individual managers are unaware of their expectations and use prior experience to base decisions on purchasing and production levels rather than a planned and co-ordinated multi-level approach. Procedures are not standardised and there is no recognition for managers that limit waste production compared to those that do not.

Description In this discussion, you will explore the zeros of polynomials. Instructions Step 1: Respond to the following: Imagine you are writing exam questions for an algebra course. You want to write questions that include finding the zeros of polynomials. To balance the difficulty level of the test’s questions, you decide to include two different types of questions, as described here: Question #1: A polynomial of degree at least 3 where all the zeros are positive whole numbers Question #2: A polynomial of degree at least 3 where one or more of the roots are fractions Find two polynomials for the two described questions. Explain how you know each question satisfies the requirements stated. What approach did you use to find these polynomials? Discussion Board 9: Vaccination and Immunity Description: Discuss the process of vaccination and how it confers immunity to the person being vaccinated. Apply this knowledge to the clinical setting to define the effectiveness and safety of vaccines. Objectives: Describe the concept of vaccination and how it produces immunity. Instructions: Step 1: Respond to the following prompts. A patient presents in your office to get their child vaccinated, and you as the healthcare provider are tasked with administering the vaccine. Before allowing their child to be vaccinated, they relay to you that they have been researching vaccination online and have concerns with regards to vaccine effectiveness and safety. What would be your response to this concerned parent? How would you support the safety and effectiveness of vaccines using statistically significant evidence? Step 2: Read other students’ posts and respond to at least two other students. Incorporate personal experience, if appropriate, to help support or debate other students’ posts. If differences of opinion occur, debate the issues and provide examples to support opinions. Be sure to cite any outside sources in current APA format. Discussion Board 9: Public Speaking Description: In this discussion, you will explore the advantages and disadvantages of self-disclosing apprehension with members of an audience. Objectives: Explore the nature of public speaking and suggestions for managing anxiety and procrastination. Identify suggestions for managing apprehension in public speaking and for overcoming procrastination. Instructions: Step 1: Respond to the following prompts: This is your first experience with public speaking and you’re very nervous. You’re afraid you’ll forget your speech and stumble. So you’re wondering if it would be a good idea to alert your audience to your nervousness. If you decide to say something, what are some things you might say? Are there advantages and disadvantages to what you might say? What would you say? What good reasons can you give to say nothing?

Your task for this discussion is as follows: Write a system of two linear equations that model something from your daily life. Solve the system of equations in two ways. Discuss which method you liked better and why. In your responses to peers, compare and contrast your preferences for how to solve systems of equations.

Statistics is about more than calculations. It is about turning data into information and using this information to understand the population. A statistician will be asked to help solve real-world problems by designing a study, collecting data, analyzing the data, and writing up the results. As a final project, you will be asked to do something similar. Though the design and data collection will be done for you, you will be asked to analyze the data using the appropriate tests (ensuring the data are distributed normally) and write up the results, using statistical evidence to support your findings. Lastly, you will be asked to include recommendations, that is, apply the results to solve the real world problem. In your paper, explain why you chose each statistical test, figure, or procedure Due to financial hardship, the Nyke Shoe Company feels they only need to make one size of shoes, regardless of gender or height. They have collected data on gender, shoe size, and height and have asked you to tell them if they can change their business model to include only one size of shoes—regardless of height or gender of the wearer. In no more than 5–10 pages (including figures), explain your recommendations, using statistical evidence to support your findings. The data found are given in the following table. Only use results in the paper. You may show your work in an appendix, if you would like

1. Build a frequency distribution table with frequencies (count), relative frequency and cumulative frequency. 2. Using Excel create the frequency table and insert a bar graph using the class interval levels and the frequencies from each class interval. 3. Create a pie chart using the relative frequencies. 4. Calculate the range 5. Calculate the mean, median, the mode 6. Calculate the sample standard deviation and variance. 7. Determine any outliers 8. Determine which is the best way to determine the average score using the mean, the median or the mode. Explain why? 9. Determine the 5 number summary. 10. Calculate the interquartile range (IQR)

.1. Let X and Y be random variables taking the values on the set 0 ? X ? Y with joint density functionfX,Y (x, y) = (4e?3xe?yfor 0 ? x ? y0 otherwise.(a) Draw the support of the joint density function. Are X and Y independent? Why or why not?(b) Find the marginal density function for Y .(c) Write a formula for the conditional density of X given that Y = y for an arbitrary value of y,fX|Y (x|y).(d) Compute the conditional expectation E(X|Y = y). The result should depend on the value of ybut not x.(e) Based on your answer to part (d), do you think the covariance of X and Y should be positive,negative, or zero? Explain.2. The number of emails I will receive as I sleep tonight is a Poisson random variable with mean 30. Eachtime I receive an email, the probability that it is spam is 0.3, independent of all other emails. Thusif I receive N emails, the number of emails which are spam is a Bin(N, 0.3) random variable. Let Nbe the number of emails I will receive tonight, and let X be the number of spam emails I will receivetonight.(a) Use “double expectation” to compute the expected value of the number of spam emails I willreceive tonight, E(X).(b) Use “double expectation” to compute the variance of the number of spam emails I will receivetonight, Var(X). You may need to use the fact that E(N2) = E(N)2+Var(N).(c) Without doing any computations, do you expect the covariance of X and N to be positive,negative, or zero? Explain why.(d) Use “double expectation” and your answer to part (a) to compute the covariance of N and X.Hint: The covariance is E(XN)?E(X)E(N). Since E(N) = 30 and you found E(X) in part (a),you just need to find E(XN). Conditioning on N, this is E(E(XN|N)) = E(NE(X|N)), sincewhen conditioning on N, we are thinking of N as a constant. You will have to use the fact thatE(N2) = E(N)2+Var(N).(e) Use your answers to parts (b) and (d) to find the correlation coefficient between X and N.. A recent NYT/Sienna poll showed that in the upcoming presidential election, 36% of Americans planto support President Trump, 50% plan to support the presumptive Democrat nominee, Joe Biden,and the remaining 14% are undecided. Assume these numbers are correct, and suppose we gather5 randomly selected Americans in a room. Find the probability that there are the same number ofTrump supporters as Biden supporters in the room. That is, if T is the number of Trump supporters,and B is the number of Biden supporters, find P(T = B).1

 Reflect on your professional or personal world. What is an example of a situation thatyou might be able to use an equation with a single unknown to help understand? What isan example of a situation that you might not be able to use an equation with a single unknown to understand? What makes an equation with a single unknown helpful in one ofyour examples but not the other? What patterns exist in your two examples that might be helpful in determining when to use a simple equation? 

Imagine that a friend is starting college and wondering whether to take calculus. The friend asks you “What does calculus have to do with the real world?” Answer the question and cite all sources that you use, including the textbook.