Answer:
a) The process seems fair because the distribution is fairly evenly spread.
Step-by-step explanation:
Point diagrams show the frequency of occurrence of a series of events after a certain number of trials. In this case the trials were 120, and the possible events were the numbers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
If all events (the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), are equally likely, the distribution of the points in the diagram should resemble a rectangle, in which all possible events have a similar number of points.
To answer this question we can start by discarding the options that are surely not correct.
Option b), for example, is incorrect.
As I mentioned before so that the process is fair, (that is to say that all the numbers have the same probability of appearing) the distribution of the points in the diagram should resemble a rectangle. If it resembled a bell it would mean that the number 5 would most likely come out.
It is true that the distribution of the points in the diagram does not completely resemble a rectangle either, and it is true that the number 8 has fewer points, in the diagram, than the rest. However, it is very difficult that with only 120 trials the number of points in the diagram is equal for all the numbers, and that the points form a rectangle. But as the number of trials increases ...
120, 200, 500, 1000, 5000 or more, the dot diagram will be more balanced, and the probability of obtaining each number will converge to the theoretical probability of P = 1/10.
So, in conclusion, for 120 trials, the points in the diagram are fairly distributed to conclude that the process is fair. The correct option is option a)
a) The process seems fair because the distribution is fairly evenly spread.
