What characteristic is least likely to be associated with a normal distribution?

What characteristic is least likely to be associated with a normal distribution?

• A. Symmetrical shape
• B. Single peak
• C. Mean, median, and mode are equal
• D. All values are equally likely

Answer: (D)

In a normal distribution, the characteristic that stands out is its symmetrical shape around the mean, single peak representing the highest frequency of data occurring at the center, and the fact that the mean, median, and mode are all equal, reflecting balance in the data. These features exemplify the properties of a normal distribution effectively. The option highlighting "all values are equally likely" does not align with the characteristics of a normal distribution. In a normal distribution, values are not equally likely; rather, values near the mean are more likely to occur than values further away. The probability density of a normal distribution is highest at the mean and decreases symmetrically as you move away from it. This means that while there is a continuous range of possible values, the likelihood of occurrence varies, confirming that this characteristic is least likely to be associated with a normal distribution.

In a normal distribution, the characteristic that stands out is its symmetrical shape around the mean, single peak representing the highest frequency of data occurring at the center, and the fact that the mean, median, and mode are all equal, reflecting balance in the data. These features exemplify the properties of a normal distribution effectively.

The option highlighting "all values are equally likely" does not align with the characteristics of a normal distribution. In a normal distribution, values are not equally likely; rather, values near the mean are more likely to occur than values further away. The probability density of a normal distribution is highest at the mean and decreases symmetrically as you move away from it. This means that while there is a continuous range of possible values, the likelihood of occurrence varies, confirming that this characteristic is least likely to be associated with a normal distribution.