Which of the following is most likely to be modeled by a $standardnormaldistribution$?

• A. The daily number of cars passing through a toll booth
• B. The number of heads in $10$ coin tosses
• C. The outcome of rolling a fair six-sided die
• D. The heights of adult men in a large population (after standardizing)

Answer: (D)

Verified step by step guidance

1. Understand what a standard normal distribution represents: it is a continuous probability distribution with a mean of 0 and a standard deviation of 1, often used to model naturally occurring continuous variables after standardization.
2. Identify the nature of each option: the daily number of cars passing through a toll booth is a count (discrete), the number of heads in 10 coin tosses is a binomial count (discrete), and the outcome of rolling a fair six-sided die is a discrete uniform variable.
3. Recognize that the heights of adult men in a large population are continuous measurements that tend to follow a normal distribution due to the Central Limit Theorem and natural biological variation.
4. Note that after standardizing (subtracting the mean and dividing by the standard deviation), the distribution of heights can be modeled by a standard normal distribution, which fits the definition perfectly.
5. Conclude that among the given options, only the standardized heights of adult men in a large population are appropriately modeled by a standard normal distribution.