Professor Potter gives a multiplechoice test with 5 choices

Professor Potter gives a multiple-choice test with 5 choices for each of 40 questions. Betty Chance did not study, so she randomly selects an answer for each question. Let X denote the number of correct answers she randomly picks. Find the standard deviation of .X

Solution

X: the number of correct choices picked

X follows binomial distribution because the answer picked is either correct or incorrect.

V(X)=npq

n=40

p=1/5

q=1-p

V(x)=6.4