Question

Suppose you roll a six-sided 50 times and calculate the mean roll, x .

We can consider these 50 rolls as a SRS of rolls from the population of all possible rolls of this die. Using formulas from Chapter 6, we can determine that if the die is fair, the mean of this population is 3.5 and the standard deviation 1.71. How would you describe the shape of this population distribution?

Answer 1

The shape of the population distribution for rolling a fair six-sided die is a uniform distribution since each outcome is equally likely.

Step-by-step explanation:

The shape of the population distribution of a fair, six-sided die's outcomes is uniform.

Since a fair six-sided die has equal probability for each of its faces, the mean of the population rolls is 3.5 with a standard deviation of 1.71.

Each face (1, 2, 3, 4, 5, 6) has an equal chance of landing, making the distribution flat and even across all possible outcomes.

The term uniform distribution reflects that all outcomes are equally likely, which is what we expect from a fair die.