PMGT3623 Scheduling - Week 5
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Questions and Answers

What is the mean (µ) of the random numbers generated by RNG2?

  • 20
  • 200
  • 130 (correct)
  • 50

    • What percentage of numbers generated by RNG2 are less than or equal to 90?

  • 99.6%
  • 97.7% (correct)
  • 95.4%
  • 68.2%

    • Which range is specified for the random numbers generated by RNG2?

  • [80 to 130]
  • [60 to 200] (correct)
  • [1 to 100]
  • [50 to 150]

    • What standard deviation (Std) is used by RNG2 in generating random numbers?

    <p>20</p> Signup and view all the answers

    In the context of RNG2, how would you describe the position of the number 80 in relation to the generated numbers?

    <p>It is below the mean</p> Signup and view all the answers

    What is the expected duration calculated from the values 10 and 20?

    <p>15 days</p> Signup and view all the answers

    What is the formula for variance given a uniform distribution?

    <p>\frac{(b - a)^2}{12}</p> Signup and view all the answers

    What is the probability density function (pdf) for a random variable X that follows a uniform distribution between a and b?

    <p>$f(x) = \frac{1}{b - a}$ for $a \leq x \leq b$</p> Signup and view all the answers

    What percentage of values falls within two standard deviations of the mean in a normal distribution?

    <p>95.4%</p> Signup and view all the answers

    What is the expected value $E[X]$ for a uniform distribution defined between a and b?

    <p>$\frac{a + b}{2}$</p> Signup and view all the answers

    What does the standard deviation indicate in a normal distribution?

    <p>How much the data points differ from the mean</p> Signup and view all the answers

    Which of the following characteristics is NOT true about the normal distribution?

    <p>All values are clustered around the median</p> Signup and view all the answers

    What is the formula for the variance $Var(X)$ of a uniformly distributed random variable?

    <p>$\frac{(b - a)^2}{12}$</p> Signup and view all the answers

    Given a task duration uniformly distributed between 10 and 20 days, what is the probability that the task will be completed within 15 days?

    <p>0.5</p> Signup and view all the answers

    What is the standard deviation formula derived from the PERT method?

    <p>\sigma = \frac{P - O}{6}</p> Signup and view all the answers

    In a normal distribution, how is the mean represented?

    <p>Mu (μ)</p> Signup and view all the answers

    What is the expected duration of a task uniformly distributed between 10 and 20 days?

    <p>15 days</p> Signup and view all the answers

    If the duration of a task is 10 to 20 days, what is the probability that it will be completed in 30 days?

    <p>1</p> Signup and view all the answers

    What does a higher standard deviation signify in relation to a data set?

    <p>Data points are more dispersed from the mean</p> Signup and view all the answers

    In modelling a project task duration uniformly between 10 and 20 days, what would be the variance?

    <p>8.33</p> Signup and view all the answers

    What is the probability of completing the task in less than 5 days given the minimum duration is 10 days?

    <p>0</p> Signup and view all the answers

    What is the main characteristic of a uniform distribution?

    <p>All outcomes are equally likely.</p> Signup and view all the answers

    Which formula represents the expected value of a uniform distribution?

    <p>$\frac{a + b}{2}$</p> Signup and view all the answers

    What is the variance formula for a continuous uniform distribution?

    <p>$\frac{(b - a)^2}{12}$</p> Signup and view all the answers

    What describes the probability of a variable taking a value less than a specific value x in a uniform distribution?

    <p>$\frac{x - a}{b - a}$</p> Signup and view all the answers

    Which of the following illustrates the discrete uniform distribution?

    <p>Rolling a fair die</p> Signup and view all the answers

    In which type of uniform distribution is the concept of continuous outcomes typically applied in project scheduling?

    <p>Continuous uniform distribution</p> Signup and view all the answers

    What is a common misconception about uniform distribution?

    <p>It can only be applied to discrete outcomes.</p> Signup and view all the answers

    What probabilistic approach would lead to biased estimation in project duration allocation?

    <p>Deterministic approach</p> Signup and view all the answers

    What statistical distribution is introduced in Week 05?

    <p>Uniform Distribution</p> Signup and view all the answers

    What method is covered in Week 06 following the Probabilistic Approach to Project Network Diagram?

    <p>Confidence Analysis</p> Signup and view all the answers

    In which week is the Knowledge Test scheduled?

    <p>Week 07</p> Signup and view all the answers

    Which of these components is weighted the heaviest in the assessments?

    <p>Final Exam</p> Signup and view all the answers

    Which approach is deemed suitable for simple projects as per the overview?

    <p>Deterministic Approach</p> Signup and view all the answers

    What is a topic discussed in Week 05 alongside Uniform Distribution?

    <p>Z-score and Z-table</p> Signup and view all the answers

    When is the Group Assignment Presentation due?

    <p>Week 12</p> Signup and view all the answers

    What type of analysis is introduced in Week 11?

    <p>Earned Value Analysis</p> Signup and view all the answers

    What is the estimated duration for the task if the company can tolerate up to 15.9% risk?

    <p>12 days</p> Signup and view all the answers

    When the company cannot afford a risk over 2.3%, what is the estimated duration for the task?

    <p>14 days</p> Signup and view all the answers

    What is the mean (μ) duration of the task in the project?

    <p>10 days</p> Signup and view all the answers

    What does a standard deviation (σ) of 2 days indicate in the context of task duration?

    <p>Most task durations will be within 2 days of the mean.</p> Signup and view all the answers

    If a company tolerates a 30% risk, can the estimated duration be found using the same method?

    <p>No, a Z-score must be used.</p> Signup and view all the answers

    How do you calculate a Z-score?

    <p>By subtracting the mean from the value and dividing by the standard deviation.</p> Signup and view all the answers

    If a student scores 16 out of 20 and another scores 30 out of 40, which method provides a fair comparison?

    <p>Converting scores to a percentage.</p> Signup and view all the answers

    What is the standard deviation (σ) value in the task's duration distribution?

    <p>2 days</p> Signup and view all the answers

    Study Notes

    PMGT3623 Scheduling - Week 5

    • Topic: Probabilistic Approach to Project Network Diagram - Part II
    • Topics Covered: Uniform Distribution, Normal Distribution (Z-score and Z-table), Project Variance and Standard Deviation
    • Uniform Distribution: Possible outcomes are equally likely. All outcomes in a specified range have an equal chance of occurring. A simple example is rolling a fair die. The probability of any score is 1/6. There are discrete and continuous uniform distributions; in project scheduling, the focus is continuous.
    • Expected Value (E): For a variable uniformly distributed between a minimum value (a) and a maximum value (b), the expected value is (a + b) / 2.
    • Variance (Var): For a uniform distribution, variance is (b - a)² / 12.
    • Probability (P(x ≤ X)): The probability of a variable taking a value less than a specific value (x) is (x - a) / (b - a), where a ≤ x ≤ b.
    • Probability Density Function (pdf): The pdf of a uniformly distributed random variable X follows f(x) = 1/(b-a) for a ≤ x ≤ b.
    • Project Variance and Standard Deviation (PERT):
      • Standard deviation (σ) = (P - O) / 6
      • Variance = (P - O)² / 36
      • Where P = Optimistic time, O=Pessimistic time
    • Normal Distribution: Often called the bell curve. Most values cluster around the mean. Frequency of values reduces symmetrically away from the mean. Defined by mean (μ) and standard deviation (σ). Mean defines the center of the distribution; standard deviation determines its spread.
    • Standard Deviation: Measures how much members of a group differ from the mean value.

    Quick Overview (Last Two Weeks)

    • Deterministic vs. Probabilistic Approaches: A deterministic approach to task duration is suitable for simple projects. In complex projects, a probabilistic approach is more accurate as it accounts for the variability in task durations. A deterministic approach often leads to biased estimation.
    • Probability Theory: Basic concepts were covered allowing for more accurate estimation.
    • Probabilistic Estimation Techniques: Expected Value and PERT (Program Evaluation and Review Technique)
    • PERT Complexity: PERT is more complex than Expected Value and uses the Beta distribution.
    • Emphasized Topics for this week: Uniform distribution, Normal distribution, and Z-score concepts.

    Additional Exercises and Examples

    • Real-world example: Example involving a project with a single task (Task A) with duration uniformly distributed between 10 and 20 days. Calculation of expected duration, variance, and probability of completing the task within specific timeframes.
    • Importance of Z-scores: How to use Z-scores to compare values from different normal distributions. Converting raw values to standard units for comparison.
    • Z-table: A table providing probabilities corresponding to different Z-scores, used for converting Z-scores to percentages and vice-versa.
    • Project Variance and Standard Deviation Exercise: Examples and calculation of the expected time, variance and standard deviation for single-task projects. Determining the probability for differing project completion timings.

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    PMGT3623 Scheduling Week 5 Lecture Plan PDF

    Description

    This quiz covers the probabilistic approach to project network diagrams, focusing on uniform and normal distributions. Key concepts include expected value, variance, and how to calculate probabilities using the uniform distribution. Test your understanding of these essential statistical methods used in project scheduling.

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