Question

Explain what's wrong with each of the following simulation designs. (a) A roulette wheel has 39 colored slots -18 red, 18 black, and 2 green. To simulate one spin of the wheel, let numbers 00 to 18 represent $x$ ed, 19 to 37 represent black, and 38 to 40 represent green. (b) About $10 \%$ of U.S. adults are left-handed. To simulate randomly selecting one adult at a time until you find a left-handed, use two digits. Let 01 to 10 represent being left-handed and 11 to 00 represent being right-handed. Move across a row in Table 10 , two digits at a time, slipping any numbers that have already appeared, until you find in number between 01 and $10 .$ Record the number of people selected.

Name: Problem 15, Chapter 5: The Practice of Statistics for AP
Uploaded: 2020-03-30T22:57:17-08:00
Duration: 3 min 34 s
Channel: Alice Simper

   Explain what's wrong with each of the following simulation designs.
(a) A roulette wheel has 39 colored slots -18 red, 18 black, and 2 green. To simulate one spin of the wheel, let numbers 00 to 18 represent $x$ ed, 19 to 37 represent black, and 38 to 40 represent green.
(b) About $10 \%$ of U.S. adults are left-handed. To simulate randomly selecting one adult at a time until you find a left-handed, use two digits. Let 01 to 10 represent being left-handed and 11 to 00 represent being right-handed. Move across a row in Table 10 , two digits at a time, slipping any numbers that have already appeared, until you find in number between 01 and $10 .$ Record the number of people selected.

The Practice of Statistics for AP

Daxen S.Starnes,… 4th Edition

Chapter 5, Problem 15

Instant Answer

Solved by Expert Alice Simper

03/30/2020

Step 1

- The roulette wheel described has 39 slots: 18 red, 18 black, and 3 green (not 2 as stated). The simulation design assigns numbers 00 to 18 for red, 19 to 37 for black, and 38 to 40 for green. However, there are only 39 slots, so the numbers should only go up to Show more…

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Explain what's wrong with each of the following simulation designs. (a) A roulette wheel has 39 colored slots -18 red, 18 black, and 2 green. To simulate one spin of the wheel, let numbers 00 to 18 represent $x$ ed, 19 to 37 represent black, and 38 to 40 represent green. (b) About $10 \%$ of U.S. adults are left-handed. To simulate randomly selecting one adult at a time until you find a left-handed, use two digits. Let 01 to 10 represent being left-handed and 11 to 00 represent being right-handed. Move across a row in Table 10 , two digits at a time, slipping any numbers that have already appeared, until you find in number between 01 and $10 .$ Record the number of people selected.

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Key Concepts

Accurate Mapping of Outcome Probabilities

A simulation must map the generated random numbers to outcomes in a way that exactly reflects the intended probabilities. In the roulette example, the numeric ranges assigned to each color do not match the actual counts of slots (e.g., assigning 19 numbers to a color that should have 18 slots), leading to a distortion of the probabilities. Accurate mapping means ensuring that each outcome receives a proportionate share reflective of the true frequencies.

Independent and Uniform Random Sampling

When simulating random events, each selection should be made independently and uniformly from the entire set of possible outcomes. The method that involves moving sequentially through a table and skipping numbers that have already appeared can introduce bias and dependency among selections. This violates the principle of independent sampling, which is crucial for maintaining the integrity of probabilistic simulations.

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