Chapter 5.1, Problem 14E

(a)

To determine

To describe how you would use slips of paper device to perform one trial of the simulation.

Explanation of Solution

In the question there is a basketball practice for each player to shoot free throws and there is a $0.70$ probability of making any free throw which corresponds with about $\text{7 out of every 10}$ shots. As,

  $\begin{array}{l}0.70\\ =\frac{70}{100}\\ =\frac{7}{10}\end{array}$

Now we will write numbers $\text{1 to 10}$ each on different slips of papers. And then,

  $\begin{array}{l}1,2,3,4,5,6,7=\text{Make free throw}\\ 8,9,10=\text{ Miss free throw}\end{array}$

Then we lie the papers on a table with the numbers facing down. And then mix the papers until you no longer know which number is where on the table. And pick one of the slips of paper. If the number is $\text{1,2,3,4,5,6 or 7}$ then the free throw was made else the free throw was missed. Now we will repeat until ten free throws were made and count the number of trials required to obtain ten free throws.

(b)

To determine

To describe how you would use random digit table device to perform one trial of the simulation.

Explanation of Solution

In the question there is a basketball practice for each player to shoot free throws and there is a $0.70$ probability of making any free throw which corresponds with about $\text{7 out of every 10}$ shots. As,

  $\begin{array}{l}0.70\\ =\frac{70}{100}\\ =\frac{7}{10}\end{array}$

Now we choose a row of the random digits table. And then select the first digits table. Then select the first digit. If the digit is between $\text{1 and 7}$ (including) then the free throw was made else the free throw was missed. So, we will repeat until ten free throws were made and count the number of trials required to obtain ten free throws.

(c)

To determine

To describe how you would use random number generator device to perform one trial of the simulation.

Explanation of Solution

In the question there is a basketball practice for each player to shoot free throws and there is a $0.70$ probability of making any free throw which corresponds with about $\text{7 out of every 10}$ shots. As,

  $\begin{array}{l}0.70\\ =\frac{70}{100}\\ =\frac{7}{10}\end{array}$

Now we will consider numbers $\text{1 to 10}$ such that:

  $\begin{array}{l}1,2,3,4,5,6,7=\text{Make free throw}\\ 8,9,10=\text{ Miss free throw}\end{array}$

Now, we enter the following command into your $\text{Ti83/Ti84}$ calculator, which will simulate $30$ shots as:

  $\text{randInt(1,10,30)}$

where randInt can be found in the MATH menu under PRB.

Thus, we will count how many numbers you need until you obtain ten digits from $\text{1 to 7}$ which thus represents that $10$ free throws were made.