The table you've provided shows the mass distribution of oranges in a crate along with their frequencies. The question asks for the probability that a randomly selected orange has a mass greater than 80 g.

Step 1: Total Number of Oranges

We need to first calculate the total number of oranges by adding all the frequencies together:

• Oranges with mass $0 < m \leq 40$: 8
• Oranges with mass $40 < m \leq 80$: 10
• Oranges with mass $80 < m \leq 120$: 11
• Oranges with mass $120 < m \leq 160$: 8
• Oranges with mass $160 < m \leq 200$: 3

Total number of oranges = $8 + 10 + 11 + 8 + 3 = 40$

Step 2: Oranges with Mass Greater than 80 g

Now, let's focus on oranges that have a mass greater than 80 g. These are represented by the frequencies for the intervals $80 < m \leq 120$, $120 < m \leq 160$, and $160 < m \leq 200$.

• Oranges with $80 < m \leq 120$: 11
• Oranges with $120 < m \leq 160$: 8
• Oranges with $160 < m \leq 200$: 3

Total number of oranges with mass greater than 80 g = $11 + 8 + 3 = 22$

Step 3: Probability Calculation

The probability is the ratio of oranges with a mass greater than 80 g to the total number of oranges:

$P(\text{mass} > 80) = \frac{22}{40} = \frac{11}{20}$

Thus, the probability that a randomly chosen orange has a mass greater than 80 g is $\frac{11}{20}$.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the probability of selecting an orange with a mass less than or equal to 80 g?
2. How would the probability change if the mass limit was raised to 120 g?
3. If you randomly select two oranges, what is the probability that both have a mass greater than 80 g?
4. What is the mean mass of the oranges in this crate?
5. How would you calculate the cumulative probability distribution for the given data?

Tip: When calculating probabilities, always ensure the event of interest is clearly defined, such as specifying ranges in cases of continuous or grouped data.