Which distribution has tails extending to infinity and is often used to describe natural phenomena?

• A. Normal Distribution
• B. Log Normal Distribution
• C. Uniform Distribution
• D. Binomial Distribution

Answer: (A)

The normal distribution is the one with tails extending to infinity in both directions. This means its density keeps stretching without a hard cutoff, though the probabilities become very small far from the center. That unbounded support makes it a natural model for many real-world measurements, because many tiny, independent factors add up to produce a result that clusters around a central value with symmetric spread.

This distribution is also especially common because of the central limit theorem: sums of many independent, small effects tend to look like a normal curve, which is why things like measurement errors, human heights, and various natural processes are often well described by it.

Other options don’t fit this description as well. A uniform distribution has a finite, fixed range, so its tails don’t extend to infinity. A lognormal distribution is defined only for positive values and is skewed, not symmetric, so its tails don’t extend in both directions the way the normal’s do. A binomial distribution is discrete with only a finite set of possible outcomes, so it’s not defined over all real numbers.