A manufacturer of headache medicine claims it is 70 percent

A manufacturer of headache medicine claims it is 70 percent effective within a few minutes. That is, out of every 100 users 70 get relief within a few minutes. A group of 12 patients are given the medicine. If the claim is true, what is the probability that 8 have relief within a few minutes?

Solution

let X be the number of patients having relief within a few minutes out of 12 patients.

so X~Bin(12,p) where p=0.70

so P[8 have relief within a few minutes]=P[X=8]=¹²C₈*0.7⁸*0.3⁴=0.231140 [answer]