Hi, this have to be completed in 6 hours.
The highly contagious Ebola virus has stricken the town of ORsville having a population of 1500. This virus has a probability of .28 of infecting each person at risk each day. A person is at risk if they currently do not have the disease and have not been effectively immunized.
A vaccine to prevent infection is available but is only 23 percent effective. That is, there is a 23 percent probability that those who are still at risk (do not have the disease and are not immunized) will be effectively immunized. Once the immunization has been effective, an individual can no longer get the disease. However, it takes 24 hours for the immunization to become effective and to determine if the immunization is effective or not. In the interim 24 hours the person may become infected with a .28 probability. If after 24 hours the person is still at risk, the person is immunized again. Each subsequent immunization has the same 23 percent chance that it will be effective.
Once infected, there is no cure. A person that is infected has a 41 percent chance of dying in each subsequent day (24 hour period).
Initially the entire town is at risk and must be quarantined. Each person will either eventually die or be successfully immunized.
The Center for Disease Control (CDC) in Atlanta has hired you as a consultant to answer the following questions:
1. What is the minimum number of survivors that can reasonably be expected?
2. What is the average (mean or expected value) that will survive?
3. What is the maximum number of survivors that can reasonably be expected?
4. What is the average number of days to complete the immunization process (i.e. there is no longer a survivor at risk - everyone is either dead or effectively immunized)?
5. What is the expected number of days until the last death occurs, and the CDC can announce that the disease has run its course.
6. If a person becomes infected, what is the expected (mean) number of days until that person dies?
In answering questions 1-3, if 1000 towns each having a population of 1500 were to contract this virus, on the average what is the minimum number of people within a town that survived from among the 1000 towns, what is the maximum number of people within a town that survived from among the 1000 towns, and what is the average number of survivors within a town from all 1000 towns?
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