A pilot study is proposed to evaluate whether a new medication is effective in c
ID: 3208251 • Letter: A
Question
A pilot study is proposed to evaluate whether a new medication is effective in controlling the symptoms of asthma. A sample of 10 patients with asthma is enrolled in the study. Each patient agrees to take the study medication and to report back in 30 days for a clinical evaluation. Similar studies report that 90% of all patient's complete follow-up visits 1 month from the initial contact. What is the distribution of X = {a number of patients show up for the clinical assessment}? What is the probability that at least 8 patients show up for the clinical assessment? What is the probability that all patients show up for the clinical assessment? What is the probability that no more than 4 patients DO NOT show up for the clinical assessment What is the probability that all show up if the true show rate is 87%? What is the expected number of patients (out of 125 patients) who DO NOT show up (if the true show rate is 87%)?Explanation / Answer
P(patient shows up) = 0.9
n = 10
a) This is a binomial distribution.
P(X = x) = 10Cx * 0.9x * (1 - 0.9)10-x
b) P(X > 8) = P(X = 8) + P(X = 9) + P(X = 10)
= 10C8 * 0.98 * 0.12 + 10C9 * 0.99 * 0.11 + 10C10 * 0.910 * 0.10
= 0.9298
c) P(X = 10) = 10C10 * 0.910 * 0.10
= 0.3487
d) P(doesn' shows up) = 1 - 0.9 = 0.1
P(no more 4 patients don't show up) = P(0 patients don't show up) + P(1 patients don't show up) + P(2 patients don't show up) + P(3 patients don't show up) + P(4 patients don't show up)
= 10C0 * 0.10 * 0.910 + 10C1 * 0.11 * 0.99 + 10C2 * 0.12 * 0.98 + 10C3 * 0.13 * 0.97 + 10C4 * 0.14 * 0.96
= 0.9984
e) P(patient shows up) = 0.87
P(X = 10) = 10C10 * 0.8710 * 0.130
= 0.2484
f) n = 125
p = 0.87
E(X) = n * p = 125 * 0.87 = 108.75 or 109 (aprrox.)
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