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

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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?

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Vivian 1 week 2021-09-15T02:49:16+00:00 1 Answer 0

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    2021-09-15T02:51:05+00:00

    Answer:

    1.844

    Step-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 = 0.2

    Similarly II group, V the no of correct answers would be binomial

    with n =10 and p = 0.25

    Our random variable X= U+V

    Obviously U and V are independent.

    We have var (U) = npq = 1.6

    Var (V) = npq = 1.875

    Var(X) = Var(U+V)

    = Var(U)+Var(V) since U and V are independent

    = 3.4

    STd dev (X) = \sqrt{3.4} \\=1.844

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