Roll 1 Die 1000 times by pressing the "Roll 100 Sets" button ten times. Then do the same for Roll 3 Dice and Roll 12 Dice. Which

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Roll 1 Die 1000 times by pressing the "Roll 100 Sets" button ten times. Then do the same for Roll 3 Dice and Roll 12 Dice. Which

best describes the sampling distributions? All three sampling distributions appear to follow the normal distribution. From left to right, the sampling distributions begin normal but then become non-normal. From left to right, the sampling distributions begin non-normal but then become more normal. All three sampling distributions appear to follow non-normal distributions.

Mathematics

2 answers:

Zina [12.3K] · Answer 1 · 2026-04-08T10:19:41+03:00

Answer:

Initially, the sampling distributions are not normal when viewed from left to right, but they ultimately trend towards normality.

Step-by-step explanation:

Referring to the prompt, we see that:

Roll 1 Die 1000 times by hitting the "Roll 100 Sets" button a total of ten times.

This process is mirrored for rolling 3 Dice and rolling 12 Dice

namely

Roll 3 Dice 1000 times by clicking the "Roll 100 Sets" button ten times.

Roll 12 Dice 1000 times by clicking the "Roll 100 Sets" button ten times.

According to the Central Limit Theorem (CLT), as the sample size increases, the sampling distribution of the mean tends to form a normal distribution.

Now, if one rolls 1 Die 1000 times where each sample comprises 100 observations.

When rolling 3 Dice in the same manner; we accumulate 3 × 100

When rolling 12 Dice similarly; we accumulate 12 × 100

This generally suggests that the sample size is increasing, leading the initially non-normal sampling distribution to become more normal over time.