Name: _________________________________ · On probability problems, you must show all work in order to earn full credit. You must define random variables and/or events and clearly identify all...

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Name: _________________________________ · On probability problems, you must show all work in order to earn full credit. You must define random variables and/or events and clearly identify all probability rules and theorems that apply. For problems involving random variables, clearly identify and explicitly justify the use of any probability distributions. Your answers must be presented in a clear, complete, systematic and logical fashion. Q1. Researchers have developed computer simulations of smallpox epidemics in small communities. The graphs below, of numbers of smallpox cases per day, illustrate the epidemics that might result under two possible containment strategies, A and B (described below). In each case, the epidemic is considered to have been started by deliberate initial infection of 500 people, simulating a possible bioterrorist attack. Strategy B: ‘Mass Vaccination + Surveillance and Containment’ (i.e. mass vaccination of 80% of the population is implemented in addition to surveillance and containment) Strategy A: ‘Surveillance and Containment Only’ (i.e. isolation of known cases and vaccination of their close contacts) The edited SAS output below shows summary statistics for the numbers of smallpox cases occurring between days 20 and 35 of the epidemics shown above. Use the output to answer the questions below. ---------------------------------- Strategy=A ---------------------------------- The UNIVARIATE Procedure Variable: Cases N 16 Sum Weights 16 Mean ? Sum Observations 404 Std Deviation ? Variance ? Corrected SS 4833 Percentile Estimate 100% Max 56.0 99% 56.0 95% 56.0 90% 51.0 75% Q3 42.5 50% 21.5 25% Q1 11.0 10% 3.0 5% 3.0 1% 3.0 0% Min 3.0 ---------------------------------- Strategy=B ---------------------------------- The UNIVARIATE Procedure Variable: Cases N 16 Sum Weights 16 Mean 9.1875 Sum Observations 147 Std Deviation 7.03532752 Variance 49.4958333 Corrected SS 742.4374995 Percentile Estimate 100% Max 22 99% 22 95% 22 90% 20 75% Q3 14 50% 7 25% Q1 4 10% 1 5% 0 1% 0 0% Min 0 a) What is the mean number of cases (rounded to 2 decimal places) for strategy A? b) What is the standard deviation of the number of cases (to 2 decimal places) for strategy A? c) What is the median number of cases (to 2 decimal places) for each strategy? d) Based on your answers above, and on the graphs and SAS output, write a brief sentence or two summarizing the data and comparing the number of smallpox cases between days 20 and 35 for the two strategies. Q2. The US National Center for Health Statistics compiles data on injuries and publishes the information in Vital and Health Statistics. Statistics show that: · 15% of injuries occur in the workplace; 85% do not occur in the workplace. · 85% of workplace injuries involve males. · 53% of non-workplace injuries involve males. All injuries involve either a male or a female. Let A be the event ‘Injury occurred in the workplace’. Let B be the event ‘Injury involved a female’. a) What percent of workplace injuries