Chapter 13.4, Problem 19PPS

a.

To determine

Find the sum of each roll.

Answer to Problem 19PPS

  $\begin{array}{cc}Trial& Sumofdie\\ 1& 4\\ 2& 7\\ 3& 11\\ 4& 4\\ 5& 6\\ 6& 4\\ 7& 5\\ 8& 9\\ 9& 9\\ 10& 8\\ 11& 3\\ 12& 7\\ 13& 2\\ 14& 12\\ 15& 6\\ 16& 2\\ 17& 10\\ 18& 6\\ 19& 9\\ 20& 7\end{array}$

Explanation of Solution

Given information:

Investigate expected value,

  

Roll two dice $20$ times.

Calculation:

Table shows the sum of $20$ rolls of a pair of dice.

  $\begin{array}{cc}Trial& Sumofdie\\ 1& 4\\ 2& 7\\ 3& 11\\ 4& 4\\ 5& 6\\ 6& 4\\ 7& 5\\ 8& 9\\ 9& 9\\ 10& 8\\ 11& 3\\ 12& 7\\ 13& 2\\ 14& 12\\ 15& 6\\ 16& 2\\ 17& 10\\ 18& 6\\ 19& 9\\ 20& 7\end{array}$

b.

To determine

Find the $20$ pairs of integers between $1\text{}and6$ .

Answer to Problem 19PPS

  $\begin{array}{cc}Trial& Sumof\mathrm{int}egers\\ 1& 9\\ 2& 5\\ 3& 3\\ 4& 4\\ 5& 6\\ 6& 12\\ 7& 3\\ 8& 7\\ 9& 8\\ 10& 8\\ 11& 3\\ 12& 2\\ 13& 2\\ 14& 12\\ 15& 6\\ 16& 2\\ 17& 10\\ 18& 12\\ 19& 9\\ 20& 6\end{array}$

Explanation of Solution

Given information:

Investigate expected value,

  

Roll two dice $20$ times.

Calculation:

Table shows the $20$ pairs of integers between $1\text{}and6$ .

  $\begin{array}{cc}Trial& Sumof\mathrm{int}egers\\ 1& 9\\ 2& 5\\ 3& 3\\ 4& 4\\ 5& 6\\ 6& 12\\ 7& 3\\ 8& 7\\ 9& 8\\ 10& 8\\ 11& 3\\ 12& 2\\ 13& 2\\ 14& 12\\ 15& 6\\ 16& 2\\ 17& 10\\ 18& 12\\ 19& 9\\ 20& 6\end{array}$

c.

To determine

Complete the table from the result of part $\left(a\right)\&\left(b\right)$ .

Answer to Problem 19PPS

  $\begin{array}{ccc}Trial& Sumof\mathrm{int}egers& SumofDie\\ 1& 9& 4\\ 2& 5& 7\\ 3& 3& 11\\ 4& 4& 4\\ 5& 6& 6\\ 6& 12& 4\\ 7& 3& 5\\ 8& 7& 9\\ 9& 8& 9\\ 10& 8& 8\\ 11& 3& 3\\ 12& 2& 7\\ 13& 2& 2\\ 14& 12& 12\\ 15& 6& 6\\ 16& 2& 2\\ 17& 10& 10\\ 18& 12& 6\\ 19& 9& 9\\ 20& 6& 7\end{array}$

Explanation of Solution

Given information:

Investigate expected value,

  

Roll two dice $20$ times.

Calculation:

Table shows the result of part $\left(a\right)\&\left(b\right)$ .

  $\begin{array}{ccc}Trial& Sumof\mathrm{int}egers& SumofDie\\ 1& 9& 4\\ 2& 5& 7\\ 3& 3& 11\\ 4& 4& 4\\ 5& 6& 6\\ 6& 12& 4\\ 7& 3& 5\\ 8& 7& 9\\ 9& 8& 9\\ 10& 8& 8\\ 11& 3& 3\\ 12& 2& 7\\ 13& 2& 2\\ 14& 12& 12\\ 15& 6& 6\\ 16& 2& 2\\ 17& 10& 10\\ 18& 12& 6\\ 19& 9& 9\\ 20& 6& 7\end{array}$

d.

To determine

Use a bar graph the number of times each possible sum occurred in the first $5$ rolls.

Answer to Problem 19PPS

  

  

  

Explanation of Solution

Given information:

Investigate expected value,

  

Repeat the process for the first $10$ rolls and then all $20$ outcomes.

Calculation:

The bar graph shows the number of times each possible sum occurred in first $5$ rolls.

  

The bar graph shows the number of times each possible sum occurred in first $10$ rolls.

  

The bar graph shows the number of times each possible sum occurred in first $20$ rolls.

  

e.

To determine

Identify the shape of a bar graph changes after each additional trial.

Answer to Problem 19PPS

The bar graph has more data points in the middle.

Explanation of Solution

Given information:

Investigate expected value,

  

Calculation:

As the trial is added each possible sum occurred in the first $20$ trials of rolling a pair of die.

The bar graph has more data points in the middle.

f.

To determine

Graph the number of times each possible sum occurred with the random number generator as a bar graph.

Answer to Problem 19PPS

/

Explanation of Solution

Given information:

Investigate expected value,

  

Calculation:

Graph the number of times each possible sum occurred in the $20$ trials of random number generator as a bar graph.

  

g.

To determine

Compare the die trial and random trial graphs.

Answer to Problem 19PPS

Both the graphs are almost similar.

Explanation of Solution

Given information:

Investigate expected value,

  

Calculation:

Both the graphs are almost similar. Both have most data point at the middle.

h.

To determine

Find excepted value based on the graphs.

Answer to Problem 19PPS

The expected value from both the experiment is the same

Explanation of Solution

Given information:

Investigate expected value,

  

Calculation:

The expected value from both the experiment is the same.