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 rocky soil prefer growing peppers?
A. 60.0%
B. 75.0%
C. 66.7%
D. 150.0%
To find the percentage chance that farmers with rocky soil prefer growing peppers, we need to use the relative frequency of the intersection between the "Rocky Soil" column and the "Peppers" row, divided by the total number of responses:
Relative frequency = 150 / 420 = 0.3571
To convert this to a percentage, we multiply by 100:
Percentage chance = 0.3571 * 100 = 35.71%
Therefore, the answer is not one of the options provided. The closest answer would be C. 66.7%, but this is incorrect.
To calculate the percentage chance that farmers with rocky soil prefer growing peppers using relative frequencies, we need to find the proportion of farmers with rocky soil who prefer growing peppers.
From the given data, we know that there are 100 farmers with rocky soil and the total number of farmers surveyed is 420. So, the relative frequency of farmers with rocky soil can be calculated as:
Relative Frequency = Number of Farmers with Rocky Soil / Total Number of Farmers
Relative Frequency = 100 / 420
Relative Frequency = 0.2381 (rounded to four decimal places)
Now, we need to find the proportion of farmers with rocky soil who prefer growing peppers. From the given data, we know that there are 150 farmers with rocky soil who prefer growing peppers. So, the proportion can be calculated as:
Proportion = Number of Farmers with Rocky Soil Who Prefer Growing Peppers / Number of Farmers with Rocky Soil
Proportion = 150 / 100
Proportion = 1.5
To express the proportion as a percentage, we multiply it by 100. So,
Percentage Chance = Proportion * 100
Percentage Chance = 1.5 * 100
Percentage Chance = 150.0%
Therefore, the correct answer is D. 150.0%.
To find the percentage chance that farmers with rocky soil prefer growing peppers using relative frequencies, we need to compare the number of farmers with rocky soil who prefer growing peppers to the total number of farmers with rocky soil.
From the given data, we can see that there are 100 farmers with rocky soil who prefer growing peppers. However, we also need to calculate the total number of farmers with rocky soil, which is the sum of the second column (120) and the third column (50), giving us a total of 120 + 50 = 170 farmers with rocky soil.
Now, we can calculate the percentage by dividing the number of farmers with rocky soil who prefer growing peppers (100) by the total number of farmers with rocky soil (170) and then multiplying by 100.
(100 / 170) * 100 = 58.8%
Therefore, the closest option is C. 66.7%.