Question

A fair six-sided die is rolled 50 times. Describe the center, shape, and spread of the sampling distribution of the proportion of even numbers rolled.

Answer 1

The center of the sampling distribution is 0.5, the shape is approximately normal, and the spread is determined by the standard error of 0.242.

Step-by-step explanation:

The center of the sampling distribution of the proportion of even numbers rolled is the expected proportion, which is 0.5 since the die is fair. The shape of the sampling distribution is approximately normal due to the central limit theorem.

The spread of the sampling distribution is determined by the standard error of the proportion. For a fair six-sided die, the standard error of the proportion can be calculated as:

1. Calculate the standard deviation of a single die roll (which is approximately 1.71 for this case).
2. Divide the standard deviation by the square root of the sample size (which is 50 in this case).

Thus, the standard error of the proportion is approximately 0.242.

Therefore, the sampling distribution of the proportion of even numbers rolled has a center of 0.5, a shape that is approximately normal, and a spread represented by the standard error of 0.242.