Dice Generator Complete Solution

Question: #1302

Dice Generator

Instructions

Please read the following scenario and answer the questions below. Use the data set below to complete this assignment. You may create your assignment using either Microsoft Word or Excel

Scenario

When playing a board game often six-sided dice are used. The numbers 1 through 6 appear on each side of the dice. Each number has an equal probability of being rolled. As mobile devices become more prevalent dice rolling apps also become more available. When comparing the theoretical probabilities to the empirical probabilities of such an app, are the probabilities the same?

Part I

Construct a probability distribution for a fair six-sided dice.
Calculate the expected value, variance, and standard deviation based on the probability distribution.

Part II

A dice simulator was used to "roll" thirty six-sided dice. The results are provided below.

2	4	2	4	3	1
4	3	3	1	5	5
6	2	2	1	1	4
4	4	3	1	5	6
1	2	3	2	5	2

Calculate the expected value, variance, and standard deviation based on the data (treat the data as a population).
Construct a probability distribution based on the data from the simulator.
Calculate the expected value, variance, and standard deviation based on the probability distribution.
Compare the values based on the data with the values based on the probability distribution. What do you notice?
Compare the empirical probabilities based on the simulator with the classical probabilities. What are the differences in the probabilities for each possible value?