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  • Perplex
    IB Math AIHL
    /
    Distributions & Random Variables
    /

    Problems

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    Problem Bank - Distributions & Random Variables

    Access custom-built, exam-style problems for distributions & random variables. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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    IB: 4
    1

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    0 / 4

    On a penalty kick, Bob scores a goal 75% of the time. Over the course of a game, Bob kicks 8 penalty kicks.

    1. Find the expected number of goals Bob scores during the game from penalty kicks.

      [1]
    2. Find the probability that Bob scores 8 goals.

      [1]
    3. Find the probability that Bob scores more than 5 goals.

      [2]
    2

    0 / 6

    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]
    3

    0 / 8

    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]
    4

    0 / 7

    Let R be the value of a roll on 6-sided die. The probability distribution for R is shown in the following table.

    r

    1

    2

    3

    4

    5

    6

    P(R=r)

    0.1

    0.1

    p

    q

    0.2

    0.2

    Sally rolls the dice 100 times, and records 25 rolls of 6.

    1. Explain why this is not inconsistent with the table.

      [1]

    Josh plays a game using this dice. He pays $4 to roll the dice, and earns back the value of his roll in dollars.

    1. Determine the value of p and the value of q such that the game is fair.

      [6]
    5

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    7
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