Given the events of 2020, the following questions all pertain to another new pandemic, n-SARS-CoV-3. Note that all the data is simulated and NOT designed to fit the data we have on Covid19, but the types of data and questions are intended to fit the framework. Problem 1. It is early in the pandemic and you have a very limited data-set that captures the number of days after infection that symptoms first show up. Name the variable X: 6 10 7 8 8 8 8 8 10 a. Calculate the following descriptive statistics. 1. Мean II. Standard deviation (s). I. Median IV. Q1 v. Interquartile Range (1QR) Q3 VI. b. Draw a histogram, such that the graph is "most" informative (in your opinion). 1. Is the histogram suggestive of a bell shape? c. Draw a box-plot, identifying and labeling the fences and any outliers. I. Are there any outliers? II. How would symptom-free patients fit into this box-plot? Problem 2. In the first three months of the pandemic, the rate at which hospitalized patients confirmed to be infected with n-SARS-CoV-3 will need a ventilator is 5%. You are responsible for a new mobile unit that has already been filled to the capacity of 120 patients. You assume that one patient's outcome is independent of every other patient, and you need to be able to plan for the number of ventilators required. Denote the number of ventilators your unit will need to treat the 120 patients as Y. Note that hacks such as doubling the number of patients per ventilator will not work in this scenario. a. How would you assume Y would be distributed, and why? b. What is the expected number of ventilators required (i.e. E(Y))? c. What is the probability that your unit will require only one ventilator (i.e. P(Y=1))? d. What is the probability that your unit will require more than one ventilator (i.e. P(Y>1))? Problem 3. Six months into the pandemic, you are running a large hospital serving a catchment area with about one million residents. The time between the arrivals of patients appears to be exponentially distributed with an average time between each arrival of 12.00000 hours. a. What is the probability that the next patient will arrive within 12.00000 hours from now? b. What is the probability that the gap between next two patients will be greater than 12.000000 hours? c. What is the probability that the gap between next two patients will be precisely 12 (with infinite zeros after the decimal) hours? d. Let Q be the number of patients that arrive per week. How is Q distributed? e. What is the probability that precisely 14 patients arrive in the next week? f. What is the probability that precisely 14 patients arrive in each of the next two weeks? 9,