Model Distributions — Tuva

Distribution:

Measures:

Axis: to

Mean 50

SD 10 max

p 0.35 n

Outcomes: vs

Attribute:

λ 3.0

Attribute:

Speed Medium

Draw Replace existing cases

Model Distributions — Introduction

Model Distributions

Pick a distribution — Normal, Binomial, Geometric, or Poisson — shape it with a small device, generate data from it, and explore that data in Tuva.

Data format

Each run writes one column to Tuva: for Normal, the values you generated (a named attribute); for Binomial, the number of successes per trial; for Geometric, the number of spins until the first success; for Poisson, the number of events in one interval. Put it on a dot plot, drop dividers, and turn on percentages — the percentage in a region is the probability of that range.

Model details

Normal draws continuous values with the mean and standard deviation you set, on an adjustable axis. Binomial spins a Success/Failure spinner n times per trial at probability p and records the count of successes. Geometric spins the same spinner until the first success and records how many spins that took; a Spin one trial button plays out a single trial. Poisson sprinkles events onto one interval at average rate λ and records how many landed. The Speed slider paces the animation. By default each Run replaces the data; uncheck “Replace existing cases” to stack runs.

Standards

HSS-ID.A.4 — Use the mean and standard deviation to fit a data set to a normal distribution and estimate population percentages; areas under the normal curve give those percentages.
HSS-MD.A.3 — Develop a probability distribution for a discrete random variable (binomial: successes in n trials; geometric: trials to the first success) and use it to find probabilities.

Design intent

Students build the distribution by direct manipulation — drag the curve’s peak and shoulders, or drag the spinner’s Success wedge — so the parameters are felt, not just typed.
The simulation only generates data; the dot plot, dividers, and percentages are the ordinary Tuva Data Tools, so “probability = the proportion in a range” is discovered with tools students already use.

Discussion prompts

On the Binomial, change p or n — how does the shape of the success-counts move and spread?
On the Geometric, lower p — how does the long right tail of “spins to first success” grow?
On the Poisson, raise λ — how does the shape shift from skewed toward symmetric?
Drop dividers and read a probability as a percentage — how does it relate to the area under the curve, or the bars, you shaped?

How do I explore?

Pick a distribution from the dropdown.
Shape it — for Normal, drag the curve’s peak (mean) and shoulders (SD); for Binomial, drag the spinner’s Success wedge to set p and choose n spins.
Press Run. Your data appears in Tuva — put it on a dot plot, drop dividers, and turn on percentages.

What should I do/notice?

As you generate more data, how does the dot plot compare to the distribution you shaped?
On Geometric, notice how often it takes many spins to reach the first success.
On Poisson, the mean of your counts lands near λ — check it on the graph.
The percentage in a region — how does it relate to the area under the curve, or the bars?

What about the data?

By default each Run replaces your data; uncheck “Replace existing cases” to stack runs. The percentage of cases in a region is the probability of that range.