1. A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ= 140+# mg/dl and σ = #+1 mg/dl, where # is the last digit of your GCU student ID number. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:Once?#+2 times, where # is the last digit of your student ID?#+4 times, where # is the last digit of your student ID?Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from the reading why this occurs and what it means in context. 2. Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 9# percent reliable, this means that the test will yield an accurate positive result in 9#% of the cases where the disease is actually present. Gestational diabetes affects #+1 percent of the population in our patient’s age group, and that our test has a false positive rate of #+4 percent. Use your knowledge of Bayes’ Theorem and Conditional Probabilities to compute the following quantities based on the information given only in part 2:If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes?What is the probability of having the disease given that you test positive?If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes?What is the probability of having the disease given that you tested negative?Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted?3. As we have seen in class, hypothesis testing and confidence intervals are the most common inferential tools used in statistics. Imagine that you have been tasked with designing an experiment to determine reliably if a patient should be diagnosed with diabetes based on their blood test results. Create a short outline of your experiment, including all of the following:A detailed discussion of your experimental design.How is randomization used in your sampling or assignment strategy?The type of inferential test utilized in your experiment.A formal statement of the null and alternative hypothesis for your test.A confidence interval for estimating the parameter in your test.An interpretation of your p-value and confidence interval, including what they mean in context of your experimental design *NOTE: USE THE ATTACHED EXCEL SHEET TO GENERATE YOUR VALUES FOR EACH PART OF THE PROJECT!This assignment uses a rubric and it should be reviewed before submission to ensure all expectations are being met.MAT 274 BENCHMARK FORMAT AND STYLE TEMPLATE

The purpose of the written assignment is to give students opportunities to apply statistical concepts to the analysis of real-world data. For this assignment, students will develop a plan to calculate descriptive statistics and generate graphs and tables from a set of real-world data.

InstructionsToday there are 195 sovereign countries in the world that are officially recognized. One can choose to look at many types of data coming from these countries, as there is a plethora of existing information. For this assignment you will be looking at populations of cities within Poland at five different times (depending on when a census was taken). The data for these cities can be found in the file named Populations. Use all of the data points for each of the years given, but please note that not every city has a population for each census.Prepare a report (see below) using the numerical methods of descriptive statistics presented in this module to show how the populations of the cities vary over the years (growth rates). Be sure to include the following three (3) items in your report.Compute descriptive statistics for each of the years along with an explanation of what the descriptive statistics tell us about the different years. Are they continually growing, or is there a decrease in the number of people? The descriptive statistics will include the mean, mode, range, standard deviation, and the 5-number summary (minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum).Determine which cities, if any, should be considered outliers in each of the years? If there are any outliers in any year, please list them and state for which year each one is an outlier. Use the z-score method to determine outliers for this question showing the z-score calculations for each city and year in your spreadsheet.Determine the correlation coefficient between the first year and each of the other years. Please provide an explanation of the relationships. Show your calculations for each correlation coefficient within the spreadsheet.Paper RequirementsWrite a report that uses the Written Assignment Requirements under the heading Expectations for CSU-Global Written Assignments found in the CSU-Global Guide to Writing and APA. Items that should be included, at a minimum, are a title page, an introduction, a body which answers the questions posed in the problem, and a conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. As with all written assignments, you should have in-text citations and a reference page. Please include any tables of calculations, calculated values, and graphs associated with this problem in the body of your assignment response.Note: You must submit your Excel file with your report. This will aid in grading with partial credit if errors are found in the report.