Allergy Sufferers 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 the patients in the study experienced insomnia as a side effect. A random sample of 20 Clarinex-D users is obtained, and the number of patients who experienced insomnia is recorded.
(a) Find the probability that exactly 3 experienced insomnia as a side effect.
(b) Find the probability that 3 or fewer experienced insomnia as a side effect.
(c) Find the probability that between 1 and 4 patients inclusive, experienced insomnia as a side effect.
(d) Would it be unusual to find 4 or more patients who experienced insomnia as a side effect? Why?