Question

A survey was designed to study how business operations vary by size. Companies were classified as small, medium, or large. Questionnaires were sent to 200 randomly selected businesses of each size. Because not all questionnaires are returned, researchers decided to investigate the relationship between the response rate and the size of the business. The data are given in the following two-way table.

What percent of all small companies receiving questionnaires responded?

a. 12.5%

b. 50.8%

c. 20.8%

d. 62.5%

e. 33.3%

Short answer

The correct option is (d)

d. 62.5%

Step-by-step solution

Step 1. Given information.

a. 12.5%

b. 50.8%

c. 20.8%

d. 62.5%

e. 33.3%

Step 2. Percent of all small businesses that received questionnaires responded

In total, 200 questionnaires were distributed to various types of businesses, with 200 of those distributed to small businesses.

Response	Small	Medium	Large
Yes	125	81	40
No	75	119	160

The number of responses for small businesses is given in the table's row with "Yes" and column with "Small," so there were 125 responses for small businesses.

As a result, 125 people responded to the 200 questionnaires.

$$\begin{gathered} \frac{125}{200}=\frac{5}{8} \\ \frac{5}{8}=0.625 \\ 0.625=62.5\% \end{gathered}$$

Thus we then note that the response rate for small companies is 62.5%

So. 62.5%

Option (d) is correct