A manufacturer of headache medicine claims it is 70% 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 eight have relief within a few minutes?
A)0.001
B)0.168
C)0.667
D)0.231

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial probability distribution. Let X be the number of patients out of 12 who get relief within a few minutes. Since each patient is independent, X follows a binomial distribution with n = 12 and p = 0.7.

To find the probability that 8 patients get relief, we can use the formula for the binomial probability:

P(X = 8) = (12 choose 8) * 0.7^8 * 0.3^4

where (12 choose 8) is the binomial coefficient, which can be calculated as:

(12 choose 8) = 12! / (8! * 4!) = 495

Substituting in the values, we get:

P(X = 8) = 495 * 0.7^8 * 0.3^4 = 0.2308 (rounded to four decimal places)

Therefore, the probability that eight patients get relief within a few minutes is 0.2308, which is closest to 0.231. Hence, the best choice is D.

A Manufacturer of Headache Medicine Claims It Is 70% Effective