Final answer:
In mathematics, a normal distribution is defined by option (D): 'The majority of scores fall in the middle range,' showing a bell-shaped curve symmetric around the mean. The standard normal distribution is normalized with a mean of 0 and standard deviation of 1. It is described using z-scores and Chebyshev's Rule for data distribution.
Step-by-step explanation:
A normal distribution is a bell-shaped distribution that is symmetric around the mean. The properties of a normal distribution include that the mean, median, and mode are all located at the same point, and the distribution is fully described by the mean (μ) and standard deviation (σ).
Option (D) 'The majority of scores fall in the middle range,' correctly defines a normal distribution because a characteristic feature of the normal distribution is that most values cluster around the mean. This implies that as you move away from the mean in either direction, the frequency of the values decreases, creating the bell-shaped curve.
The standard normal distribution is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. It represents standardized scores called z-scores. The area under the curve of the normal distribution equals one since it's a continuous distribution.
A z-score indicates how many standard deviations a score is from the mean, and can be used to compare scores from different distributions. It is calculated using the formula z = (x - μ) / σ.
Chebyshev's Rule provides that a certain percentage of data falls within a specific number of standard deviations from the mean, across all distributions. For a normal distribution, approximately 68% of the data lies within one standard deviation of the mean, about 95% within two standard deviations, and 99.7% within three standard deviations.
Learn more about Normal Distribution here: