Chapter 24, Problem 20E

(a)

To determine

Section 1:

To find: The percentage of all attempted field goals made by Seth Fitzgerald.

Answer to Problem 20E

Solution: The required percentage is 53.33%.

Explanation of Solution

Calculation:

The percentage of field goals made by Seth Fitzgerald can be calculated as a ratio of the number of attempts, which are made by Seth Fitzgerald and total number of all attempted field goals by Seth Fitzgerald in a multiple of 100.

The total number of attempted field goal is calculated as:

$\begin{array}{c}\text{Total field goals}=5+4+3+3\\ =15\end{array}$

The total number of field goals made by Seth Fitzgerald is calculated as:

$\begin{array}{c}\text{Total field goals made}=5+3\\ =8\end{array}$

Therefore, the required percentage is calculated as:

$\begin{array}{c}\text{Percentage}=\frac{\text{Total field goals made}}{\text{Total field goals }}\times 100\\ =\frac{8}{15}\times 100\\ =53.33\%\end{array}$

Section 2:

To find: The percentage of all attempted field goals made by Roberto Mantovani.

Solution: The required percentage is 53.84%.

Calculation:

The percentage of field goals made by Roberto Mantovani can be calculated as a ratio of the number of attempts that are made by Roberto Mantovani and total number of all attempted field goals in a multiple of 100.

The total number of attempted field goal is calculated as:

$\begin{array}{c}\text{Total field goals}=62+50+1+4\\ =117\end{array}$

The total number of field goal made by Roberto Mantovani is calculated as:

$\begin{array}{c}\text{ Total field goals }=62+1\\ =63\end{array}$

Therefore, the required percentage is calculated as:

$\begin{array}{c}\text{Percentage}=\frac{\text{Total field goals made}}{\text{Total field goals attempted }}\times 100\\ =\frac{63}{117}\times 100\\ =53.84\%\end{array}$

(b)

Section 1:

To determine

To find: The percentage of two-point and three-point field goals by Seth Fitzgerald.

Answer to Problem 20E

Solution: The percentages of two-point and three-point field goals are 55.56% and 50%.

Explanation of Solution

Calculation:

The percentage of two-point and three-point field goals can be calculated as a ratio of the number of attempts that are made by Seth Fitzgerald and the number of two-point and three-point field goals in a multiple of 100.

The total number of two-point attempted field goals by Seth Fitzgerald is calculated as:

$\begin{array}{c}\text{Two-point field goals}=5+4\\ =9\end{array}$

The number of two-point field goals made is 5.

Therefore, the percentage of two-point field goals is calculated as:

$\begin{array}{c}\text{Percentage of two-point field goals}=\frac{\text{Two-point field goals made}}{\text{Total two-point field goals attempted }}\times 100\\ =\frac{5}{9}\times 100\\ =55.56\%\end{array}$

The number of three-point attempted field goals is calculated as:

$\begin{array}{c}\text{Three-point field goals}=3+3\\ =6\end{array}$

The number of three-point field goals made is 3.

Therefore, the percentage of three-point field goals made is calculated as:

$\begin{array}{c}\text{Percentage of three-point field goals}=\frac{\text{Three-point field goals made}}{\text{Total three-point field goals attemted }}\times 100\\ =\frac{3}{6}\times 100\\ =50\%\end{array}$

Section 2:

To find: The percentage of two-point and three-point field goals by Roberto Mantovani.

Solution: The percentages of two-point and three-point field goals are 55.35% and 20%.

Explanation:

Calculation:

The percentage of two-point and three-point field goals made by Roberto Mantovani can be calculated as a ratio of the number of attempts that are made by Roberto Mantovani and the number of two-point and three-point field goals attempted in a multiple of 100.

The total number of two-point attempted field goals by Roberto Mantovani is calculated as:

$\begin{array}{c}\text{Two-point field goals}=62+50\\ =112\end{array}$

The number of two-point field goals made is 62.

Therefore, the percentage of two-point field goals is calculated as:

$\begin{array}{c}\text{Percentage of two-point field goals}=\frac{\text{Two-point field goals made}}{\text{Two-point field goals attemted }}\times 100\\ =\frac{62}{112}\times 100\\ =55.35\%\end{array}$

The number of three-point field goals is calculated as:

$\begin{array}{c}\text{Three-point field goals}=1+4\\ =5\end{array}$

The number of three-point field goals made is 1.

Therefore, the percentage of three-point field goals is calculated as:

$\begin{array}{c}\text{Percentage of three-point field goals}=\frac{\text{Three-point field goals made}}{\text{Three-point field goals attempted}}\times 100\\ =\frac{1}{5}\times 100\\ =20\%\end{array}$

(c)

To determine

To explain: The reason for which the provided statement is correct though its sounds to be impossible.

Answer to Problem 20E

Solution: As the number of goals made by Robert is more compared to the individual type of goals, the overall percentage is better.

Explanation of Solution

The overall field goals made by Roberto is 53.84%. But Roberto made 55.35% two-point field goals and 20% of three-point field goals. The percentage of three-point goals is much lower than the overall percentage as well as percentage of two-point goals, because Robert made only one three-point goal out of 5 attempts. But the overall percentage is better because Robert made total 63 goals out of 117 attempts.