Question

frederick designed an experiment in which he spun a spinner 20 times and recorded the results of each spin. spinner image with sections labeled 1,2,3,4,5,6,7,8,9,10 he spun a 4 five times. which statements are true? choose all that apply. ☐ for the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased. ☐ for the experimental outcomes to be closer to the predicted outcome, the number of trials should be

Explanation:

1. The spinner has 10 equal - sized sections (numbers 1 - 10). The theoretical probability of spinning a 4 is $\frac{1}{10}$. In 20 trials, the expected number of times to spin a 4 is $20\times\frac{1}{10}=2$. But in the experiment, it was spun 5 times.
2. According to the Law of Large Numbers, as the number of trials (spins) increases, the experimental probability gets closer to the theoretical (predicted) probability. So, to make the experimental outcomes closer to the predicted outcome, the number of trials should be increased. The second statement (about decreasing the number of trials) is wrong because decreasing trials would make the result more erratic.

Answer:

The true statement is: "For the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased." (The checkbox next to this statement should be selected)