Chapter 0.6, Problem 30E

a.

To determine

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

Answer to Problem 30E

The percent correct on the test if W scored 72 points is $81.8\%$ .

Explanation of Solution

Given information:

The provided table depicts the points scored by students in a math test in W’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 W’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 W’s percent correct on test, since he scored 72 points so, 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, W scored is $81.8\%$ in math test.

b.

To determine

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

Answer to Problem 30E

The percent correct on the test if C scored 81 points is

  $92.0\%$ .

Explanation of Solution

Given information:

The provided table depicts the points scored by students in a math test in W’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 W’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 C’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, C scored is $92.0\%$ in math test.

c.

To determine

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

Answer to Problem 30E

The percent correct on the test if R scored 75 points is

  $85.2\%$ .

Explanation of Solution

Given information:

The provided table depicts the points scored by students in a math test in W’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 W’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 R’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, R 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 test is $98.9\%$ and $77.3\%$ respectively.

Explanation of Solution

Given information:

The provided table depicts the points scored by students in a math test in W’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 W’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 M has scored the highest point and Penny has scored the lowest point.

For M’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, M 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.