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

45.5%
45.5%

100.0%
100.0%

83.3%
83.3%

40.0%
40.0%
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Answer 1

To find the percentage chance that a farmer who prefers to grow carrots has rocky soil, we need to use the relative frequency of farmers with rocky soil who prefer carrots compared to the total number of farmers who prefer carrots.

From the table:

• The number of farmers with rocky soil who prefer carrots = 100
• The total number of farmers who prefer carrots = 220

Now, we calculate the relative frequency:

\[ \text{Relative frequency} = \frac{\text{Number of rocky soil carrot farmers}}{\text{Total number of carrot farmers}} = \frac{100}{220} \]

Now, we convert this fraction to a percentage:

\[ \frac{100}{220} \approx 0.4545 \]

To convert this to a percentage, we multiply by 100:

\[ 0.4545 \times 100 \approx 45.45% \]

Rounding this to the nearest tenth gives us 45.5%.

So the answer is:

45.5%