Question

Use the table to answer the question.

Figuring out what proportion of rocky-soil farmers choose to produce pepper

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 farmers with sandy soil prefer to grow carrots? Round your answer the nearest tenth.

A. 60.0%
B. 75.0%
C. 66.7%
D. 150.0%

Answer 1

To find the percentage chance that farmers with sandy soil prefer to grow carrots, we need to calculate the relative frequency of sandy soil farmers growing carrots.

1. From the table, we can see that:
- The number of sandy soil farmers who grow carrots = 120
- The total number of sandy soil farmers = 170

2. The relative frequency (or probability) that a sandy soil farmer grows carrots is calculated as follows:
\[
\text{Relative Frequency} = \frac{\text{Number of sandy soil farmers growing carrots}}{\text{Total number of sandy soil farmers}} = \frac{120}{170}
\]

3. Calculating this value:
\[
\frac{120}{170} \approx 0.70588
\]

4. To convert this to a percentage, multiply by 100:
\[
0.70588 \times 100 \approx 70.588
\]

5. Rounding to the nearest tenth gives us:
\[
\approx 70.6\%
\]

Since this percentage does not match any of the provided options exactly, it seems that the closest and likely intended answer among the choices is **C. 66.7%**, although the calculated answer was approximately 70.6%.

You might want to double-check the options available, as none match the computed probability exactly.