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Binomial Probability Concepts and Distributions

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Probability Concepts and Distributions:
[6] In a clinical trial of Lipitor, a common drug used to lower cholesterol, 863 patients were given a treatment of 10-mg Atorvastatin tablets. Among them, 19 patients experienced flu symptoms and 844 patients did not (based on data from Pfizer, Inc.).
a) What would you think that the most appropriate distribution is to apply to the situation? Explain why.
Answer: Since there is a natural rate of occurrence flu (say x number of people per 1000 Q1: Prof: (???) Why not 863?) which may be assumed to be reasonably constant, poisson distribution is the most appropriate distribution to be applied.
b) Estimate the probability that a patient taking the drug will experience flu symptoms.
Answer:

Q2: Prof: Your answer, meaning above is not correct?
c) Is this unusual for a patient taking the drug to experience flu symptoms in (b)? Explain.
Answer:
Yes, it is unusual for a patient taking a drug to experience flu symptoms since there is only a 2.15% probability that the patient will experience the flu. When you compare that to the CDCs average for the population contracting the flu it is 5%.
Q3: Prof: How could you know that the chance of getting such symptoms is ONLY 2.15%, which you sounded that it was too small to ignore? Why would you think that 2.15% is insignificant in this situation?

e) Is this unusual to find that among 863 patients, there are 19 who experience flu symptoms in d)? Explain.
Answer:
Yes this is unusual to find of 863 patients that 19 would experience flu symptoms since, using the binominal distribution the probability and a success rate of .019, the probability of 19 individuals experiencing flu like symptoms .0754
Binomial Probabilities

Data
Sample size 863
Probability of an event of interest 0.019

Statistics
Mean 16.397
Variance 16.0855
Standard deviation 4.0107

Q4: Prof So you are saying that this time 0.0754 is significant, aren't you? What argument did you use in [4] c) when asked "usual" or not?

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Binomial probability concepts and distributions are examined for multiple questions.

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[6] In a clinical trial of Lipitor, a common drug used to lower cholesterol, 863 patients were given a treatment of 10-mg Atorvastatin tablets. Among them, 19 patients experienced flu symptoms and 844 patients did not (based on data from Pfizer, Inc.).
a) What would you think that the most appropriate distribution is to apply to the situation? Explain why.
Answer: Poisson distribution can be used in this situation if we know the average rate of getting flu. If we know the average rate of getting flu, then the probability of ...

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