Clarinexd is a medication whose purpose is to reduce the sym

Clarinex-d is a medication whose purpose is to reduce the symptoms of associated eith a variety of allergies . In clinical trials of clinical trials clarinex-d, 5% of the patients in the study experience insomnia as a side effect. A random sample 20 clarinex-d users is selected and the number of patients who experience insomnia is recored. 1) find the probability that exactly 3 experience insomnia as a side effect. 2) find the probability 3 or fewer experience insomnia. 3) find the probability between 1 and 4 experience insomnia. 4) would it be unusual to find 4 or more patients experience insomnia as side effect.

Solution

Proportion population as per estimate = 5% =0.05

Sample sizez = 20

X- no of persons suffering insomnia is binomial with (20, 0.05)

1) P(x=3) = 20C3 (0.05)³(0.95)¹⁷

= 0.0596

2) P(X<=3) = 0.9841

3) P(1<x<4) = 0.9841-0.7358

= 0.2483

4) P(X>=4) = 0.0159

Hence not very unusual.