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    IB Math AASL
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    Distributions & Random Variables
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    Distributions & Random Variables

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    Thumbnail for Discrete random variables

    Introduction and properties of random variables, probability distributions, expected value and variance, linear transformations of r.v.'s

    Discrete random variables
    Thumbnail for Binomial Distribution

    Concept of the binomial distribution, binomial PDF and CDF, expectation and variance of binomial distribution

    Binomial Distribution (Plus Only)
    Thumbnail for Normal Distribution

    Introduction and definition of the normal distribution, standard deviations, normal and inverse normal calculations, z-values, normal standardization

    Normal Distribution (Plus Only)

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    IB: 4
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    The masses, in grams, of chocolate bars produced by a factory can be modelled by a normal distribution with mean 100g and standard deviation 0.6g. A chocolate bar can only be packaged if its mass is greater than 99g, otherwise is it melted back into the production line.

    1. Find the probability that a randomly selected chocolate bar is packaged.

      [2]

    On a given day, the number of chocolate bars packaged is 5000.

    1. Estimate, to the nearest 10, the number of chocolate bars that are melted back that day.

      [3]
    2. Given that a bar has a mass of less than 101g, find the probability it will be melted down.

      [3]
    2

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    James is sitting a multiple choice exam with 15 questions. Each question has 3 answer choices, of which only one is correct.


    James randomly picks an answer on each question. Let X represent the number of questions James answers correctly.

    1. State whether X is discrete or continuous.

      [1]
    2. Write down the value of E(X).

      [1]
    3. Find the probability that

      1. X=7,

        [1]
      2. 3<X<10.

        [3]

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