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What is characteristic of a normal distribution in a population?

  1. It shows equal variation

  2. It requires linearity

  3. It exhibits a bell-shaped curve

  4. It displays skewed data

The correct answer is: It exhibits a bell-shaped curve

A normal distribution is characterized primarily by its bell-shaped curve, representing how data points are distributed around the mean. This shape indicates that most of the observations cluster around the central peak, with fewer observations appearing as you move further away from the mean in either direction. The standard deviation in a normal distribution defines the width of the bell curve, with a smaller standard deviation indicating that the data points are closer to the mean, and a larger standard deviation indicating more spread out data. In contrast to this, the other options do not accurately describe the key traits of a normal distribution. For example, equal variation does not apply, as normal distributions encompass varying degrees of spread as indicated by the standard deviation. Linearity pertains more to relationships between variables rather than the distribution of a single variable. Lastly, skewed data represents a deviation from normality, where data points do not symmetrically balance around the mean, which stands in direct opposition to the concept of a normal distribution. Thus, the bell-shaped curve remains the defining visual and statistical characteristic of a normal distribution.