A company developed a new shampoo to reduce dandruff Six per

A company developed a new shampoo to reduce dandruff. Six persons tried that shampoo. Assume that the probability that a person gets some relief is 0.60. Let X be the number of persons out of the six who find some relief. Determine the probability distribution of the random variable X and then find its mean and variance.

Solution

X is a Binomial distribution with parameters n=6 and p=0.60

P(x) =6Cx(0.6)^x(0.4)^(6-x)         x=0,1,2, ... , 6

The mean of x =np=6*0.6 =3.6

Variance is np(1-p)= 6*0.6*0.4 =1.44