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Use the table to answer the 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%

45.5%
45.5%

40.0%
40.0%

100.0%

1 answer

To determine the percentage of farmers who prefer producing carrots and have rocky soil, we need to calculate the relative frequency using the data provided in the table.

  1. Identify the number of farmers who prefer carrots with rocky soil:

    • From the table, the number of farmers with rocky soil who prefer carrots = 100.

  2. Identify the total number of farmers who prefer carrots:

    • The total number of farmers who prefer carrots = 220 (as per the "Totals" column).

  3. Calculate the relative frequency: \[ \text{Relative Frequency} = \frac{\text{Number of farmers with rocky soil who prefer carrots}}{\text{Total number of farmers who prefer carrots}} = \frac{100}{220} \] \[ \text{Relative Frequency} = \frac{100}{220} \approx 0.4545 \]

  4. Convert to percentage: \[ \text{Percentage} = 0.4545 \times 100 \approx 45.5% \]

Thus, the percentage chance that if a farmer prefers to grow carrots they have rocky soil is 45.5%.

The correct response is: 45.5%