Chapter 0.6, Problem 30E

a.

To determine

To calculate: The percent correct on the test if Will scored 72 points.

Answer to Problem 30E

The percent correct on the test if Will scored 72 pointsis $81.8\%$ .

Explanation of Solution

Given information:

The provided table depicts the points scored by students in a math test in Will’s study group.

  $\begin{array}{cccccc}\text{Name}& \text{Will}& \text{Penny}& \text{Cheng}& \text{Minowa}& \text{Rob}\\ \text{Score}& 72& 68& 81& 87& 75\end{array}$

Formula used:

Percent proportion is ratio of amount and base is same as percent to 100.

To convert percentage to fraction divide the number by 100.

Calculation:

Consider the provided table that depicts the points scored by students in a math test in Will’s study group.

  $\begin{array}{cccccc}\text{Name}& \text{Will}& \text{Penny}& \text{Cheng}& \text{Minowa}& \text{Rob}\\ \text{Score}& 72& 68& 81& 87& 75\end{array}$

For Will’s percent correct on test, since he scored 72 pointsso, evaluate what percent 72 is of 88.

Recall that percent proportion is ratio of amount and base is same as percent to 100.

According to the question, number of score point divided by total number of points is desired percent correct,

  $\begin{array}{c}\frac{72}{88}=\frac{x}{100}\\ x=\frac{72\times 100}{88}\\ x=81.\overline{81}\\ x=81.8\end{array}$

Thus, Will scored is $81.8\%$ in math test.

b.

To determine

To calculate: The percent correct on the test if Cheng scored 81 points.

Answer to Problem 30E

The percent correct on the test if Cheng scored 81 pointsis $92.0\%$ .

Explanation of Solution

Given information:

The provided table depicts the points scored by students in a math test in Will’s study group.

  $\begin{array}{cccccc}\text{Name}& \text{Will}& \text{Penny}& \text{Cheng}& \text{Minowa}& \text{Rob}\\ \text{Score}& 72& 68& 81& 87& 75\end{array}$

Formula used:

Percent proportion is ratio of amount and base is same as percent to 100.

To convert percentage to fraction divide the number by 100.

Calculation:

Consider the provided table that depicts the points scored by students in a math test in Will’s study group.

  $\begin{array}{cccccc}\text{Name}& \text{Will}& \text{Penny}& \text{Cheng}& \text{Minowa}& \text{Rob}\\ \text{Score}& 72& 68& 81& 87& 75\end{array}$

For Cheng’s percent correct on test, since he scored 81 points so, evaluate what percent 81 is of 88.

Recall that percent proportion is ratio of amount and base is same as percent to 100.

According to the question, number of score point divided by total number of points is desired percent correct,

  $\begin{array}{c}\frac{81}{88}=\frac{x}{100}\\ x=\frac{88\times 100}{81}\\ x=92.0\overline{45}\\ x=92.0\end{array}$

Thus, Cheng scored is $92.0\%$ in math test.

c.

To determine

To calculate: The percent correct on the test if Rob scored 75 points.

Answer to Problem 30E

The percent correct on the test if Rob scored 75 pointsis $85.2\%$ .

Explanation of Solution

Given information:

The provided table depicts the points scored by students in a math test in Will’s study group.

  $\begin{array}{cccccc}\text{Name}& \text{Will}& \text{Penny}& \text{Cheng}& \text{Minowa}& \text{Rob}\\ \text{Score}& 72& 68& 81& 87& 75\end{array}$

Formula used:

Percent proportion is ratio of amount and base is same as percent to 100.

To convert percentage to fraction divide the number by 100.

Calculation:

Consider the provided table that depicts the points scored by students in a math test in Will’s study group.

  $\begin{array}{cccccc}\text{Name}& \text{Will}& \text{Penny}& \text{Cheng}& \text{Minowa}& \text{Rob}\\ \text{Score}& 72& 68& 81& 87& 75\end{array}$

For Rob’s percent correct on test, since he scored 75 points so, evaluate what percent 75 is of 88.

Recall that percent proportion is ratio of amount and base is same as percent to 100.

According to the question, number of score point divided by total number of points is desired percent correct,

  $\begin{array}{c}\frac{75}{88}=\frac{x}{100}\\ x=\frac{75\times 100}{81}\\ x=85.2\overline{27}\\ x=85.2\end{array}$

Thus, Rob scored is $85.2\%$ in math test.

d.

To determine

To calculate: The highest and lowest percentage in math test.

Answer to Problem 30E

The highest and lowest percentage in math testis $98.9\%$ and $77.3\%$ respectively.

Explanation of Solution

Given information:

The provided table depicts the points scored by students in a math test in Will’s study group.

  $\begin{array}{cccccc}\text{Name}& \text{Will}& \text{Penny}& \text{Cheng}& \text{Minowa}& \text{Rob}\\ \text{Score}& 72& 68& 81& 87& 75\end{array}$

Formula used:

Percent proportion is ratio of amount and base is same as percent to 100.

To convert percentage to fraction divide the number by 100.

Calculation:

Consider the provided table that depicts the points scored by students in a math test in Will’s study group.

  $\begin{array}{cccccc}\text{Name}& \text{Will}& \text{Penny}& \text{Cheng}& \text{Minowa}& \text{Rob}\\ \text{Score}& 72& 68& 81& 87& 75\end{array}$

Observe that Minowa has scored the highest point and Penny has scored the lowest point.

For Minowa’s percent correct on test, since he scored 87 points so, evaluate what percent 87 is of 88.

Recall that percent proportion is ratio of amount and base is same as percent to 100.

According to the question, number of score point divided by total number of points is desired percent correct,

  $\begin{array}{c}\frac{87}{88}=\frac{x}{100}\\ x=\frac{87\times 100}{88}\\ x=98.8\overline{63}\\ x=98.9\end{array}$

Thus, Minowa scored is $98.9\%$ in math test.

For Penny’s percent correct on test, since he scored 68 points so, evaluate what percent 68 is of 88.

Recall that percent proportion is ratio of amount and base is same as percent to 100.

According to the question, number of score point divided by total number of points is desired percent correct,

  $\begin{array}{c}\frac{68}{88}=\frac{x}{100}\\ x=\frac{68\times 100}{88}\\ x=77.\overline{27}\\ x=77.3\end{array}$

Thus, Penny scored is $77.3\%$ in math test.

Hence, the highest and lowest percentage in math test is $98.9\%$ and $77.3\%$ respectively.