Question

one hundred thirty people were asked to determine how many cups of fruit and water they consumed per day. the results are shown in the frequency table. identify the conditional relative frequency by row. round to the nearest percent. the conditional relative frequency that someone ate more than 2 cups of fruit, given the person drank less than or equal to 4 cups of water is approximately. the conditional relative frequency that someone ate less than or equal to 2 cups of fruit, given the person drank more than 4 cups of water is approximately. | | ≤ 2 cups of fruit | > 2 cups of fruit | total | |---|---|---|---| | ≤ 4 cups of water | 62 | 20 | 82 | | > 4 cups of water | 18 | 30 | 48 | | total | 80 | 50 | 130 |

Explanation:

Step1: Calculate first conditional relative frequency

To find the conditional relative frequency that someone ate more than 2 cups of fruit, given the person drank less than or equal to 4 cups of water, we use the formula for conditional relative frequency by row: $\text{Conditional Relative Frequency} = \frac{\text{Frequency of the joint event}}{\text{Total of the row}}$. For the row "≤ 4 Cups of Water", the number of people who ate more than 2 cups of fruit is 20, and the total of this row is 82. So we calculate $\frac{20}{82} \approx 0.2439$, which is approximately 24% when rounded to the nearest percent.

Step2: Calculate second conditional relative frequency

For the conditional relative frequency that someone ate less than or equal to 2 cups of fruit, given the person drank more than 4 cups of water, we use the same formula. For the row "> 4 Cups of Water", the number of people who ate less than or equal to 2 cups of fruit is 18, and the total of this row is 48. So we calculate $\frac{18}{48} = 0.375$, which is 38% when rounded to the nearest percent (or 37.5% which rounds to 38%).

Answer:

The conditional relative frequency that someone ate more than 2 cups of fruit, given the person drank less than or equal to 4 cups of water is approximately 24%.
The conditional relative frequency that someone ate less than or equal to 2 cups of fruit, given the person drank more than 4 cups of water is approximately 38%.