Chapter 6.1, Problem 39IP

a.

To determine

Find the percentage of students surveyed that the instrument was playing.

Answer to Problem 39IP

The percentage of students are $12.5\%$ .

Explanation of Solution

Given:

It is given in the question that the number of students playing instruments are $80$ and the total number of respondents is $640$ .

Concept Used:

In this, use the concept of percent proportion such that the ratio of given two number will equal to the ratio of $p/100$ .

Calculation:

Here,

Total number of respondents: $198+150+212+80=640$

  $\begin{array}{l}\frac{80}{640}=\frac{p}{100}\\ p\cdot 640=80\cdot 100\\ p=\frac{80\times 100}{640}\\ p=\frac{8000}{640}\\ p=12.5\%\end{array}$

Conclusion:

The percentage is $12.5\%$ .

b.

To determine

Find whether the percentage of the stand up comedy will greater than, less than, or equal to the percent line, if $10$ more votes increase.

Answer to Problem 39IP

It will increase if $10$ more votes will increase in standup comedy.

Explanation of Solution

Given:

It is given in the question that the number of student of standup comedy $198$ .

Concept Used:

In this, use the concept of percent proportion such that the ratio of given two number will equal to the ratio of $p/100$ .

Calculation:

Here,

  $\begin{array}{l}\frac{198}{640}=\frac{p}{100}\\ p\cdot 640=198\cdot 100\\ p=\frac{198\times 100}{640}\\ p=\frac{19800}{640}\\ p\approx 30.9\%\end{array}$

About $30.9\%$ of the students voted for standup comedy.

Now, for second case, $198+10=208$ also increase for total $640+10=650$ .

  $\begin{array}{l}\frac{208}{650}=\frac{p}{100}\\ p\cdot 650=208\cdot 100\\ p=\frac{208\times 100}{650}\\ p=\frac{20800}{650}\\ p=32\%\end{array}$

About $32\%$ of the students voted for standup comedy in this case.

So, it will increase if $10$ more votes will increase in standup comedy.

Conclusion:

It will increase if $10$ more votes will increase in standup comedy.