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    The random variable X has a binomial distribution with parameters n and p.It is given that E(X) = 3.5.

    Question
    HLPaper 2

    The random variable X has a binomial distribution with parameters n and p.
    It is given that E(X) = 3.5.

    1.

    Find the least possible value of n.

    [2]
    Verified
    Solution

    * This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

    np= 3.5 (A1)

    p ≤ 1 ⇒ least n= 4 A1

    [2 marks]

    2.

    It is further given that P(X ≤ 1) = 0.09478 correct to 4 significant figures.

    Determine the value of n and the value of p.

    [5]
    Verified
    Solution

    (1− p)n + np(1−p)n−1 = 0.09478 M1A1

    attempt to solve above equation with np= 3.5 (M1)

    n = 12, p = 7 24 (=0.292) A1A1

    Note: Do not accept n as a decimal.

    [5 marks]

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