The probability of flu symptoms for a person not receiving any treatment is 0.03

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, 35 of 1051 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that at least 35 people experience flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the drug? (a) P(X greaterthanorequalto 35) = (Round to four decimal places as needed.)

Explanation / Answer

With binomial distribution,

p = 0.03 , n = 1051

mean = np = 1051 * 0.03 = 31.53

SD = sqrt(np(1-p)) = sqrt(1051*0.03*0.97) = 5.5303

With binomial continuity correction,

p(X>= 35) = p(X>34.5)

= p ( Z > 34.5 - 31.53 / 5.5303)

= p( Z> 0.537)

= 1 - p(z< 0.537)

= 1 - 0.7044

= 0.2956

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