1. Mathematical models are used as tools to describe reality. These models are supposed to characterize the important features of the analyzed phenomena and provide insight. The normal distribution is an example of a random variable that is widely used by researchers to model real data. Researchers often model real observations using the normal distribution, but sometimes the real distribution is a bit different from the perfect, normal distribution. List some reasons why researchers might make approximations like this and describe at least one situation when researchers should not use this approximation. When forming your answer to this question you may give an example of a situation from you own field of interest for which a random variable can serve as a model. (2-3 well composed paragraphs) 2. Describe in your own words the meaning of the number that the following R command produces (you are asked to interpret the resulting number so that we understand what that number means). pexp(1.2, rate=3) (1 paragraph) 3. Vocabulary and R functions (be sure to include an APA citation) a) What is a normal distribution? _________________ b) What does the pnorm() function do?_________________________ 4. If you know the mean and standard deviation of a normally distributed population, and somebody asks you questions about the highest 1% and lowest 1% of numbers in that population, what could you tell them? Pick your own values for the mean and standard deviation and then answer the question for those values. Choose one of these R functions to answer the question: dnorm(), pnorm(), qnorm(), rnorm(). (2-3 well composed paragraphs)

Question 1: We have received a set of comments over time on the web. Check if we have improved? Please note that there are no pre- and post intervention periods and therefore control limits must be calculated from the entire period. You can find the data hereYou can find the solution here here - Alternative Formats .Question 2: The following data show the speed with which Alabama Medical Center's Emergency Room provides a patient who has fractured long bone with pain medication. Examine if the organization has been able to reduce the response time to less than 73 minutes? You can find the data hereMeasure Start DateMeasure End DateMinutes to Pain MedicationSample4/1/20133/31/2014781327/1/20136/30/2014681247/1/20136/30/20146812410/1/20139/30/2014721221/1/201412/31/2014761384/1/20143/31/2015851447/1/20146/30/20158613710/1/20149/30/2015951211/1/201512/31/201599111Please use the following peer video as a reference for this question. You can find the solution here here - Alternative Formats .Question 3: In Hospital Administration Programs, time to adverse events is typically taught in courses on quality. It also may be referred to in courses on strategy, if the hospital is focused on competing based on quality. Hospital Compare reports the measure OP_21. The Score field provides time (in minutes) from emergency department arrival to initial oral, intranasal or parenteral pain medication administration for the patients with a diagnosis of a long bone fracture. The field Sample provides the number of patients used to calculate the time to pain medication. In this assignment, we ask you to track the performance of "Inova Fairfax Medical Center" over two years. Focus on the Score variable. Download Hospital Compare data; these years include data from 2013 to 2015. Merge the file " HQI_HOSP_TimelyEffectiveCare" across all the databases that you have downloaded. Select measure ID: "OP_21" . Construct a control chart showin time between pain medications. The data are reported for a range of time; assume that the data are reported for the midpoint of the range. Download data using the following files, additionally include other data (directly from Hospital Compare) for files after 2016: 2016-11-10 2016-08-10 2016-05-04 2015-12-10 2015-10-08 2015-07-16 2015-05-06 2015-04-16 2015-01-22Construct both a Tukey and a time-between control chart for the data. For the time-between control chart assume that data points above median exceed and observations below median are less than the national average.You can find the solution here here - Alternative Formats .Question 4: Analyze the following data using Tukey and Time-In-Between (more than 30 minutes of exercise considered a successful day) charts. Produce 3 charts and discuss if the findings from the 3 charts are similar. To decide if the exercise time has changed, rely on the control chart with the smallest difference between upper and control limit. Download the data hereYou can find the solution here here - Alternative Formats .