4. Final exam has 20 multiple choices questions. 10 questions have 5 choices and 10 questions have 4 choices. In each question, only one of the choices is the correct answer. Now assume that you just randomly pick the choices. If X is the number of questions which you choose the right answer, what is the standard deviation of X?

Answer:1.844Step-by-step explanation:Given that final  exam has 20 multiple choices questions. 10 questions have 5 choices and 10 questions have 4 choices.So we divide the questions into two groups I and II.The no of correct answers in I is called U.U is binomial with n =10 and p = 0.2Similarly II group, V the no of correct answers would be binomialwith n =10 and p = 0.25Our random variable X= U+VObviously U and V are independent.We have var (U) = npq = 1.6Var (V) = npq = 1.875Var(X) = Var(U+V)= Var(U)+Var(V) since U and V are independent= 3.4STd dev (X) = [tex]\sqrt{3.4} \\=1.844[/tex]