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.

Explanation:

Step1: Recall conditional - relative - frequency formula

The formula for conditional relative frequency by row is $\frac{\text{Frequency in cell}}{\text{Row total}}$.

Step2: Calculate first conditional relative frequency

We want 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. The frequency of people who drank $\leq4$ cups of water and ate $> 2$ cups of fruit is 20, and the total number of people who drank $\leq4$ cups of water is 82. So the conditional relative - frequency is $\frac{20}{82}\approx0.244$. Rounding to the nearest percent, it is 24%.

Step3: Calculate second conditional relative frequency

We want to find 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. The frequency of people who drank $>4$ cups of water and ate $\leq2$ cups of fruit is 18, and the total number of people who drank $>4$ cups of water is 48. So the conditional relative - frequency is $\frac{18}{48}=0.375$. Rounding to the nearest percent, it is 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%.