Question

A binomial distribution has two outcomes: success and failure.  

I have to create a binomial distribution problem relevant to the field of psychology.

Answer 1

Imagine that the proportion of school going children that face depression is 5%. Let us take a sample of 6 school going kids. We need to find the probability that there are exactly 2 children in the sample that have depression. Let X be the number of children in the sample that face depression.

Probability of sucess, p = Proportion of children with depression = 0.05

q = 1 - p = 0.95

Number of trials, n = 6

Binomial distribution: P(X) = nCx p^x q^n-x

P(2 children in the sample have depression), P(X = 2) = 6C2 x 0.05² x 0.95⁴

= 0.0305