Question

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.

Answer 1

all three sampling distributions appear to follow the normal distribution

Explanation:

Sampling distribtuions follow a normal distribution.

Answer 2

From left to right, the sampling distributions begin non-normal but then become more normal.

Explanation:

If we refer back to our question, we are being told that:

Roll 1 Die 1000 times by pressing the "Roll 100 Sets" button ten times.

The same is done for Roll 3 Dice and Roll 12 Dice

i.e

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

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

From the knowledge of Central Limit Theorem (CLT), we understand that the sampling distribution of a given sample mean usually approaches a normal distribution as the sample size gets larger.

Now, if we roll 1 Die 1000 times in which every sample has 100 observations.

If 3 Dice is rolled the same way; we have 3 × 100

If 12 Dice is rolled the same way; we have 12 × 100

This typically implies that the sample size gets increasing , thus the sampling distribution begins non-normal but then becomes more normal.