Practice Problem Assignment - Probability

1. You are planning an experiment with combination drug therapy. You have four different medications, Alphacillin, Betacillin, Chicillin and Deltacillin. You want to do a trial testing the various combination of patients taking two of the drugs at a time. Each unique combination of two drugs will be a study group. How many groups will you need to test all possible combinations of two drugs? You MUST show all work to receive credit!

2. From number 1 (above) list the unique combination groups that will be tested in this study. 

3. You have been asked to assess a community where the residents feel that they are seeing a higher than expected number of cases of autism in their children. They feel that the nearby paper processing plant and its chemical waste are to blame. The rate of autism in the communities outside of the suspect community is .10. You draw a random sample of 20 children and 2 of them have autism. What is the probability of seeing 2 or more autistic cases in these circumstances? You MUST show all work to receive credit!

4. From number 3 (above) state whether you think there is an issue of an unusually high rate of autism that bears further investigation or if the rate is what would be expected by chance. 

5. You have a sample with a mean of 10 and a standard deviation of 2. What is the z-score for the subject with a value of 2 on the given variable?