Question

The probability of flu symptoms for a person not receiving any treatment is 0.03. In a clinical trial of a common drug used to lower​ cholesterol, 37 of 1143 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu​ symptoms, estimate the probability that at least 37 people experience flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the​ drug?

Answer 1

P(flu), p = 0.03

Sample size, n = 1143

Normal approximation to the binomial: P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = np

= 1143 x 0.03

= 34.29

Standard deviation =

=

= 5.7673

P(at least 37 people experience flu symptoms), P(X 37) = 1 - P(X < 36.5)       (with continuity correction)

= 1 - P(Z < (36.5 - 34.29)/5.7673)

= 1 - P(Z < 0.38)

= 1 - 0.6480

= 0.3520

The probability of at least 37 people experiencing flu symptoms is not an unusual event because the probability is greater than 0.05. Therefore, there is no evidence to suggest that flu symptoms are caused as an adverse reaction to the drug.