A new drug has been found to be effective in treating 50% of the people afflicted by a certain disease. If the drug is administered to 800 people who have this disease, what is the standard deviation of the number of people for whom the drug can be expected to be effective?
A) 14.19
B) 14.11
C) 14.06
D) 14.14
E) 14.15

Question

Quizplus · Accepted Answer

Given, probability of drug being effective = 0.5

Number of people = 800

The number of people for whom the drug can be effective follows a binomial distribution with parameters n = 800 and p = 0.5.

The mean of the binomial distribution = np = 800 x 0.5 = 400

The variance of the binomial distribution = np(1-p) = 800 x 0.5 x 0.5 = 200

The standard deviation of the binomial distribution = sqrt(np(1-p)) = sqrt(200) = 14.14 (approx)

Therefore, the answer is D) 14.14.

A New Drug Has Been Found to Be Effective in Treating