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Suppose a certain treatment has a known response rate of 65% amongst adults. Further, suppose we randomly select 5 new adult patients to receive treatment. You may assume that these patients are independent.
a) How many patients would you expect to be responders?
b) What is the variance on the number of responders from the sample? Calculate the following probabilities (c-f):
c) The first three patients are responders and the last two patients are not responders. (Note: Exactly this sequence)
d) Any three patients are responders and two are not responders.
e) Three or more patients are responders.
f) At least one patient responds to the treatment.
g) Give two examples of how the assumptions of the binomial distribution could be violated if this were a real life situation.
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