A biotechnology firm was exploring safety concerns in a new drug already on the

Question

A biotechnology firm was exploring safety concerns in a new drug already on the market that could lower systolic blood pressure by an average of 16 mm-Hg. A small survey of patients found that 75% of individuals taking this drug reported mild to severe migraines after taking the drug for at least two weeks. Assuming the survey result holds for the entire population of patients taking this drug, what’s the probability that in a sample of fifteen patients taking the drug for at least 2 weeks, between 5 and 9 individuals (inclusive) will experience migraines of some severity?

Explanation / Answer

This will be a binomial experiment with parameters:

n = 15, p = 0.75

q = 1 - p = 1 - 0.75 = 0.25

Hence,

P(Between 5 and 9 individuals)

= P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)

= 15C5 (0.75)5(0.25)10 + 15C6 (0.75)6(0.25)9 + 15C7 (0.75)7(0.25)8 + 15C8 (0.75)8(0.25)7 + 15C9 (0.75)9(0.25)6

= 0.1483 [Rounded off to 4 decimal places]

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