In this topic you move from describing continuous distributions to actually computing with them. For a continuous random variable, probability is area under the density curve, so every calculation reduces to finding an area between two points, to the left of a point, or to the right of a point. For the uniform distribution that area is a rectangle you can find geometrically; for the exponential distribution it comes from a short closed-form cumulative distribution function; for the normal distribution it requires converting values to z-scores and then reading a table or using technology.
These skills matter because almost every applied problem in this course ends with a probability statement that someone has to act on: the chance a component lasts beyond its warranty period, the chance a measurement falls outside specification limits, the chance a wait time exceeds a service target. Getting the number right is only half the job; you also need to state clearly what the number means in context and what decision it supports.
While watching, pay close attention to three things. First, how each presenter sets up the problem: which parameters are identified, and how the question is translated into an area. Second, which table or technology convention is used, since normal tables differ (mean-to-z versus cumulative-from-the-left) and mixing them up is one of the most common errors. Third, the small habits that prevent mistakes: sketching the curve and shading the region, checking that your answer is between 0 and 1, and confirming that the answer is on the plausible side of 0.5 given where your cutoff sits relative to the mean.
This video demonstrates normal probability calculations using a mean-to-z table, meaning the table entries give the area between the mean and a given z-value rather than the full cumulative area. It shows how to convert raw values to z-scores and then combine or subtract table areas to find left-tail, right-tail, and between-two-values probabilities, with a note on doing the same work on a Casio calculator.
It squarely covers z-score conversion and table use, and because it uses the mean-to-z convention it is a useful check on whether you truly understand what your own table reports instead of copying numbers mechanically.
Reviewing this uniform distribution video a second time is useful for the error-avoidance subtopic: watch specifically for how interval endpoints are handled and how the problem statement is turned into limits of integration or rectangle boundaries.
Repeated, focused viewing of a clear worked example is an efficient way to internalize the setup step, which is where most calculation errors actually originate.
A short lesson on the exponential distribution from the LearnChemE project at the University of Colorado Boulder, aimed at engineering students. It should introduce the density and cumulative distribution function in terms of the rate or mean parameter and apply them to computing probabilities, typically for waiting times or times between events.
LearnChemE materials are produced by engineering faculty and framed around engineering applications, so the examples connect the exponential CDF to the kinds of lifetime and interarrival problems you will see in this course.
Together these three videos cover the computational core of the module. The uniform and exponential videos reinforce MO1 by showing how a density function and its cumulative form are used to produce probabilities, and all three directly serve MO2 by demonstrating the formulas, z-score conversion, and CDF evaluations for the three required distributions. Because each video frames its calculations around concrete scenarios, they also support MO3 by illustrating the kinds of situations each distribution is meant to model, and MO4 by modeling how a computed number is stated back in context. Use them alongside the module's worked examples, and practice sketching and labeling each region before you compute.
These videos were chosen from YouTube on October 2, 2026. Each has captions; the player turns them on. Videos on YouTube can be changed or removed — if one no longer plays, tell your instructor. If a player does not appear, use its Watch on YouTube link.