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  • Perplex
    IB Math AASL
    /
    Distributions & Random Variables
    /

    Problem Bank

    [Maximum mark: 8]

    A random variable ​X​ is normally distributed with a mean ​μ​ of ​70​ and standard deviation ​σ.

    ​
    X∼N(70,σ)
    ​
    1. Determine with justification which of the following could be the value of ​P(X>90). List all that apply.

      ​0​

      ​0.03​

      ​0.5​

      ​0.66​

      ​0.97​

      [2]

      To earn a crown, get your answer ready before you reveal the options!

    It is given that ​P(X>80)=0.17.

    1. Find the value of

      1. ​P(60<X<80)​

        [2]
      2. ​P(X>80∣X>70).

        [2]
    2. Using your answer to (b.i), determine which of the following options is closest to the value of ​σ.

      ​0.5​

      ​3​

      ​11​

      ​25​

      [2]

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