Can I get help on this please? I'm not getting this.

Question

Suppose it is believed that the probability a patient will recover from a disease following medication is 0.8. In a group of twenty such patients, the number who recover would have mean and variance respectively given by (to one decimal place):

Mean: 

Variance:

Answer 1

P(Recover) = 0.8, where the probability is a success.

n = 20 patients in a group

X ~ Binomial (20, 0.8)

E(X) = np = (20)(0.8) = 16

V(X) = npq = (20)(0.8)(0.2) = 3.2 (Note: q is the failure probability, where q = 1 - p)

The expected number of patients who recovered from the disease is 16 and the variance is about 3.2.