1. The question is consisted of 2 parts.
Part 1 asks us for
the number of groups such that "the majority of the occurrences of cooperative behaviors were observed within the first 50 seconds of the observation".
Part 2 asks us for
the number of groups such that "the number of occurrences of cooperative behaviors within the first 50 seconds was greater than 15".
2.
Part 1. Counting the number of observations in each group would waste too much time. So, we can estimate by looking at the area beneath 50 seconds and above.
-
Group A. The area beneath 50 seconds is about \(\frac{1}{3}\) of the total area. \(\frac{1}{3} \leq \frac{1}{2}\),
so it's not the majority.
-
Group B. The area beneath 50 seconds looks more than \(\frac{1}{2}\) of the total area.
So, the majority is under 50 seconds.-
Group C. Here, the area beneath 50 seconds is a little bit more than \(\frac{1}{3}\) of the total area, however, it's definitely less than \(\frac{1}{2}\) of the total area.
So, it's not the majority.-
Group D. The area beneath 50 seconds is less than the area in 100 - 150 seconds.
So, it's not the majority.3.
Part 2. Here we can estimate too but sometimes we might have to count.
-
Group A. This is too close to say, so we calculate it: 1 + 1 + 2 + 1 + 6 = 11 \(\leq\) 15.
So, this group doesn't count.-
Group B. There are two bars that are at least 12 each: Area \(\geq 12 * 2 = 24 > 15\).
So, this group does count.-
Group C. We have 1 bar that's at least 12 and 3 that are at least 4 each: Area \(\geq 12 + 4 * 3 = 24 > 15\).
So, this group does count.-
Group D. We have 2 bars with at least 8 each: Area \(\geq 8 * 2 = 16 > 15\).
So, this group does count.4. That means our answer is Part 1 -
1 group and Part 2 -
3 groups.