What is a normal distribution?

What is a normal distribution?

• A. A distribution with equal probabilities for all outcomes.
• B. A distribution that is skewed toward the right.
• C. A discrete uniform distribution.
• D. A symmetric bell-shaped curve.

Answer: (D)

The normal distribution is a continuous, symmetric, bell-shaped curve. It peaks at the mean and is perfectly mirrored around that center, so the mean, median, and mode are all the same. Probabilities accumulate smoothly toward the center and taper off toward the tails, and the shape is determined by the mean and standard deviation. This symmetric, unimodal form is what defines a normal distribution and why many statistical methods assume it. The other descriptions don’t fit: equal probabilities for all outcomes describe a uniform distribution, which is flat rather than bell-shaped; a distribution skewed toward the right is not symmetric; a discrete uniform distribution involves a finite set of outcomes with equal probabilities, not a continuous, bell-shaped curve.

The normal distribution is a continuous, symmetric, bell-shaped curve. It peaks at the mean and is perfectly mirrored around that center, so the mean, median, and mode are all the same. Probabilities accumulate smoothly toward the center and taper off toward the tails, and the shape is determined by the mean and standard deviation. This symmetric, unimodal form is what defines a normal distribution and why many statistical methods assume it.

The other descriptions don’t fit: equal probabilities for all outcomes describe a uniform distribution, which is flat rather than bell-shaped; a distribution skewed toward the right is not symmetric; a discrete uniform distribution involves a finite set of outcomes with equal probabilities, not a continuous, bell-shaped curve.