Clarinex-D is a medication whose purpose is to reduce the symptoms associated wi
ID: 3177918 • Letter: C
Question
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) Can the binomial model be used to answer questions below? List all assumptions for binomial distribution model, and check if they are all met in this problem (b) Find the probability that exactly 3 experienced insomnia as a side effect. Use the formula for the number of successes in the binomial distribution (c) Find the probability that 3 or fewer experienced insomnia as a side effect. You may use the calculator. Write down detailed command or show calculations. (d) Find the probability that between 1 and 4 patients inclusive, experienced insomnia as a side effect Write down detailed command, or show calculations (e) What is the expected value and standard deviation of the number of patient who experienced insomnia as a side effect? Show work (as above) (f) Would it be unusual to find 4 or more patients who experienced insomnia as a side effect? Why? ExplainExplanation / Answer
Solution:-
a) Yes, Binomial can be used for this question.
Assumptions for binomial distribution:-
1) Each replication of the process results in one of two possible outcomes (success or failure),
2) The probability of success is the same for each trial.
3) Each trial are independent, probability of success does not effect the probability of success of other trial.
b) The probability that exactly 3 experienced insomnia as a side effect is 0.05958.
Probability of insomnia as side effect = 5/100 = 0.05
Number of trials = 20
By applying binomial distribution:-
P(x, n, p) = nCx * px * (1 - p)(n - x)
P(x = 3) = 0.05958
c) The probability that 3 or fewer experienced insomnia as a side effect is 0.9841
Probability of insomnia as side effect = 5/100 = 0.05
Number of trials = 20
By applying binomial distribution:-
P(x, n, p) = nCx * px * (1 - p)(n - x)
P(x < 3) = 0.9841
d) The probability that between 1 and 4 patients inclusive, experienced inxomnia as side effects is P(1 < x < 4) = 0.6256.
Probability of insomnia as side effect = 5/100 = 0.05
Number of trials = 20
By applying binomial distribution:-
P(x, n, p) = nCx * px * (1 - p)(n - x)
P(1 < x < 4) = P(x > 1) - P(x > 4)
P(1 < x < 4) = 0.6415 - 0.0159
P(1 < x < 4) = 0.6256