Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of patients in the study experienced insomnia as a side effect of taking the medication. Suppose a random sample of 20 patients who took Clarinex-D is obtained and the number of patients who experienced insomnia, X, is recorded. For parts (b)-(d), write a probability statement, such as P(X>3), and calculate the probability (either by hand or using software). Be careful of the wording. Know the difference between less than, at most, etc. Required:
a. What are the possible values of X?
b. Find the probability that exactly 3 experience insomnia as a side effect?
c. Find the probability 3 or fewer experience insomnia?
d. Between 1 and 4 experience insomnia.
e. Would it be unusual to find 4 or more patients experience insomnia as a side effect?