Which of the following can be reasonably modeled by a $normaldistribution$?

• A. The heights of adult men in a large population
• B. The number of heads in $10$ flips of a fair coin
• C. The outcome of rolling a fair $6$-sided die
• D. The day of the week chosen at random

Answer: (A)

Verified step by step guidance

1. Understand what a normal distribution represents: it is a continuous probability distribution characterized by a symmetric, bell-shaped curve, often used to model natural phenomena where values cluster around a mean with some variability.
2. Evaluate each option to see if it fits the characteristics of a normal distribution:
3. 1. Heights of adult men in a large population: This is a continuous variable with natural variation around an average height, often approximately normally distributed due to the Central Limit Theorem and biological variation.
4. 2. Number of heads in 10 flips of a fair coin: This is a discrete variable representing a binomial distribution, which counts the number of successes in a fixed number of trials, not continuous and not normally distributed for such a small number of trials.
5. 3. Outcome of rolling a fair six-sided die: This is a discrete uniform distribution where each outcome (1 through 6) is equally likely, not continuous and not bell-shaped.
6. 4. Day of the week chosen at random: This is a categorical variable with seven equally likely categories, not continuous and not normally distributed.
7. Conclude that only the heights of adult men in a large population can be reasonably modeled by a normal distribution.