Question

s paragraph for the following short answer questions.
a game piece that has six sides numbered 1 through 6. a student calculates that when the die is tossed, the probability of rolling a \5\ is equal to one out of six, or 1/6, or 0.17. to
y, the student tosses the die 20 times, and rolls a \5\ 2 out of 20 times.
paragraph above, what was the sample size used by the student?
es the result the student got after tossing the die compare to the theoretical/calculated probability?
on your answer, what can you infer about the sample size used by the student? explain your answer.

Explanation:

Sub - question 1: What was the sample size used by the student?

Step 1: Recall the definition of sample size

Sample size is the number of times an experiment is repeated. In this case, the student tossed the die 20 times. So the sample size is the number of tosses.

The theoretical probability of rolling a "5" on a fair six - sided die is $P=\frac{1}{6}\approx0.17$. The experimental probability the student got is $\frac{2}{20} = 0.1$. Since $0.1<0.17$, the experimental probability (the result the student got) is less than the theoretical probability.

In probability experiments, as the sample size (number of trials) increases, the experimental probability tends to get closer to the theoretical probability (by the Law of Large Numbers). The student's experimental probability (0.1) is different from the theoretical probability (≈0.17). Since the sample size here is 20 (which is relatively small), we can infer that with a small sample size, the experimental results can deviate from the theoretical probability. If the sample size were larger, the experimental probability would likely be closer to the theoretical probability of $\frac{1}{6}$.

Answer:

20

Sub - question 2: How does the result the student got after tossing the die compare to the theoretical/calculated probability?