Homework SourseClarinexD is a medication whose purpose is to reduce the sym
Clarinex-D is a medication whose purpose is to reduce the symptom associated with a variety of allergies. In a clinical trial of 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 recorded. A) Find the probability that exactly 3 experience insomnia as a side effect? B) Find the probability 3 or fewer experience insomnia? C) Between 1 and 4 experience insomnia. D) Would it be unusual to find 4 or more patients experience insomnia as a side effect?
Clarinex-D is a medication whose purpose is to reduce the symptom associated with a variety of allergies. In a clinical trial of 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 recorded. A) Find the probability that exactly 3 experience insomnia as a side effect? B) Find the probability 3 or fewer experience insomnia? C) Between 1 and 4 experience insomnia. D) Would it be unusual to find 4 or more patients experience insomnia as a side effect?
Clarinex-D is a medication whose purpose is to reduce the symptom associated with a variety of allergies. In a clinical trial of 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 recorded. A) Find the probability that exactly 3 experience insomnia as a side effect? B) Find the probability 3 or fewer experience insomnia? C) Between 1 and 4 experience insomnia. D) Would it be unusual to find 4 or more patients experience insomnia as a side effect?
Solution
poisson with lambda = 0.05 * 20 = 1
a ) P(X = 3 ) = e^(-1) / 3! = 0.0613
b ) P(X <= 3) = summation (e^(-1) / x!) x = 0 to 3 = 0.981
c ) P(1 <= X <= 4) = summation (e^(-1) / x!) x = 1 to 4 = 0.628
d ) P(X >= 4) = 1 - P(X<=3) = 1 - 0.981 = 0.019 , hence unusual
