Question

The National Institute of Mental Health reports that 20% of adult Americans suffer from a psychiatric disorder. Suppose we randomly select 6 adult Americans. What is the probability that exactly 2 of them suffer from a psychiatric disorder? Round your answer to 4 decimal places.

Answer 1

Solution :

Given that ,

p = 0.20

1 - p = 1 -0.20 = 0.80  

n = 6

X = 2

Using binomial probability formula ,

P(X = x) = ((n! / (n - x)!) * p^x * (1 - p)^{n - x}

P(X = 2) = ((6! / (6 - 2)!) *0.20² * 0.80^{6 -2}

= 0.2458

Probability = 0.2458