Use the table to answer the question.

Question

Determining the percentage of farmers with rocky soil who prefer producing carrots.
Carrots Peppers Totals
Sandy Soil 120 50 170
Rocky Soil 100 150 250
Totals 220 200 420
Examine the data from a survey of farmers about their different soil types and the crops they prefer to grow. Using relative frequencies, what is the percentage chance that if a farmer prefers to grow carrots they have rocky soil? Round your answer to the nearest tenth.

(1 point)
Responses

83.3%
83.3%

40.0%
40.0%

45.5%
45.5%

100.0%

Answer 1

To determine the percentage of farmers with rocky soil who prefer producing carrots, we can use the relative frequency based on the data provided.

First, we need to identify the total number of farmers who prefer carrots and how many of those have rocky soil:

1. Total number of farmers who prefer carrots: 220 (from the "Carrots" total)
2. Number of farmers with rocky soil who prefer carrots: 100 (from the "Rocky Soil" row, "Carrots" column)

Now, we can calculate the percentage of farmers who prefer carrots that have rocky soil:

\[ \text{Percentage} = \left(\frac{\text{Number of Rocky Soil Carrot Farmers}}{\text{Total Carrot Farmers}}\right) \times 100 \]

Substituting the numbers:

\[ \text{Percentage} = \left(\frac{100}{220}\right) \times 100 = 45.454545\ldots \]

Rounding to the nearest tenth, the percentage is approximately 45.5%.

Thus, the correct response is:

45.5%