1. Clarinex-D is a medication whose purpose is to reduce the symptoms associate

Question

1. Clarinex-D is a medication whose purpose is to reduce the symptoms associate 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 experience insomnia as a side effect.

B.) Find the probability that 3 or fewer experiences insomnia as a side effect.

C.) Find the probability that between 1 and 4 patients, inclusive, experienced insomnia as a side effect.

Explanation / Answer

p = 0.05

n = 20

P(X = x) = 20Cx * 0.05x * (1 - 0.05)20-x

a) P(X = 3) = 20C3 * 0.053 * 0.9517 = 0.0596

b) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

                  = 20C0 * 0.050 * 0.9520 + 20C1 * 0.051 * 0.9519 + 20C2 * 0.052 * 0.9518 + 20C3 * 0.053 * 0.9517

                  = 0.9841

c) P(1 < X < 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

                         = 20C1 * 0.051 * 0.9519 + 20C2 * 0.052 * 0.9518 + 20C3 * 0.053 * 0.9517 + 20C4 * 0.054 * 0.9516

                         = 0.6389

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