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135
3.3
Probability Distributions
P
urpose
The role this topic plays in quantitative reasoning
In mathematics, we love patterns of behavior. We like to study, analyze, and model behaviors. Many
behaviors have randomness, but is there a pattern in this randomness? The study of random behaviors
that fall into patterns has led to the identification and quantification of different probability distributions.
The study of probabilistic phenomena, modeling of behaviors, predicting the future, and explaining the
past is strongly based on our understanding of these different probability distributions. It is highly likely
that a strong quantitative reasoning performance will involve and use the concepts of randomness and
probability distributions.
Randomness pervades even the simplest phenomenon and probability distributions can summarize this
fuzzy behavior into coherent pictures. From observed data one can sometimes create a model from
“off-the-shelf” distributions or discover something seemingly new. Often the connection is made that
situations in disparate disciplines both follow the same pattern of randomness providing insight into the
sub-aspects of a problem.
L
earning Goals
What you should learn while completing this activity
1. See how each type of probability distribution reflects a unique pattern of randomness.
2. Determine the type of probability distribution that best represents a set of collected data.
3. Learn that different types of real-life situations commonly match certain distributions.
D
iscovery
Finding out for yourself
What pattern do you think the following random phenomena follow (let’s say if you
repeated each phenomenon 500 times)?
1. The total showing after rolling a pair of dice?
2. The number of heads when flipping multiple coins at once?
3. The final location of a bean falling through the bean machine shown at right?
Use simulations such as those found on the companion website to validate
your guesses.
4. What distributions do these behaviors actually follow?
5. Did the results surprise you? Did the patterns follow what you expected?