Use a random number table or a computer to simulate rolling...

Name: Problem 22, Chapter 4: Elementary Statistics
Uploaded: 2020-06-03T00:26:13-08:00
Duration: 4 min 38 s
Channel: Robin Corrigan
Description: Use a random number table or a computer to simulate rolling a pair of dice 100 times. a. List the results of each roll as an ordered pair and a sum. b. Prepare an ungrouped frequency distribution and a histogram of the sums. c. Describe how these results compare with what you expect to occur when two dice are rolled.

Use a random number table or a computer to simulate rolling a pair of dice 100 times. a. List the results of each roll as an ordered pair and a sum. b. Prepare an ungrouped frequency distribution and a histogram of the sums. c. Describe how these results compare with what you expect to occur when two dice are rolled.

Use a random number table or a computer to simulate rolling a pair of dice 100 times.
a. List the results of each roll as an ordered pair and a sum.
b. Prepare an ungrouped frequency distribution and a histogram of the sums.
c. Describe how these results compare with what you expect to occur when two dice are rolled.

Key Concepts

Simulation

Simulation involves creating a model of a random process using either a random number table or computer software to generate outcomes. This method is used to mimic real-life random experiments and helps in observing possible outcomes and their distribution over multiple trials.

Sample Space Representation

In the context of rolling dice, the sample space is represented by ordered pairs depicting the result from each die. This clear organization of outcomes is crucial to understanding all possible events and is a foundational concept in probability theory.

Frequency Distribution

A frequency distribution is a summary that shows the number of times each outcome or range of outcomes occurs in a data set. When simulating dice rolls, it allows one to compare the observed frequencies of each sum to their expected probabilities, thereby illustrating the randomness of the process.

Histogram

A histogram is a graphical representation of the frequency distribution. It visually displays the number of occurrences for each sum outcome from the simulated dice rolls. This visualization aids in quickly identifying patterns or discrepancies when comparing to theoretical expectations.

Expected Probabilities and Theoretical Comparison

Comparing the simulation results with expected outcomes involves understanding the probabilities associated with each sum of two dice. This concept ties into the law of large numbers, where as the number of trials increases, the observed frequencies should approach the theoretical probabilities derived from the known properties of dice.

Transcript

00:01 In this problem, we simulate rolling a pair of dice 100 times.

00:05 So part a is to list the dice rolls along with the sum of the dice.

00:11 So we use minutab to do this.

00:13 So we can go to calculate random data, integer.

00:24 And so we're going to make 100 generations of data.

00:29 And we're going to do it twice once for each dice.

00:32 So we'll store the first set of 100 in column c1, and the second set of 100 in column c2.

00:39 We set the minimum value equal to 1 and the maximum value equal to 6 to simulate a die roll.

00:46 And we hit ok.

00:48 So now you can see in column c1 and c2, we have simulated die rolls.

00:54 And now we want to sum the dice in column c3.

00:58 So we go to calculate calculator.

01:03 And i've entered an expression c1 plus c2.

01:07 And we can store that outcome in column c3.

01:13 So once we do that, we have the sums of the dice rolls.

01:17 So the first row was a 5 and a 1, and the sum is a 6.

01:21 The second row was a 2 and a 2, and the sum is a 4.

01:26 So basically, you can provide this list as your answer to part a, where column c1 and c2 are the ordered pairs of dice rolls, and column c3 is the sum.

01:41 So for b, we're asked to present an ungrouped frequency distribution and a histogram of the sums.

01:49 So we can do this by going to calculate.

01:58 Actually, that's under stat, pavos, pali individual variables.

02:07 And so we select the sums row.

02:09 That's the sums column.

02:11 That's column c3...

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