In a clinical research study, the heights of a sample of 200 individuals are measured. If the distribution of these heights follows a normal distribution, which of the following statements is true?
The correct answer is:
C) The majority of individuals in the sample will have heights close to the mean.
In a normal distribution, the majority of data points are concentrated around the mean, with fewer data points distributed further away from the mean. This is characterized by the bell-shaped curve of the normal distribution.
Answer choice A: All individuals in the sample will have the exact same height, is incorrect. In a normal distribution, individual values vary, and it is highly unlikely that all individuals in the sample will have the exact same height. Variability is a fundamental characteristic of a normal distribution.
Answer choice B: The heights in the sample will be evenly distributed across a wide range, is incorrect. A normal distribution is not characterized by an even distribution of data across a wide range. It has a specific shape with the majority of data clustered around the mean.
Answer choice D: The median of the heights will be greater than the mean. In a normal distribution, the median is equal to the mean. There is no inherent relationship that suggests the median must be greater than the mean.
Answer choice E: The standard deviation of the heights will be zero. The standard deviation of the heights in a normal distribution is not zero; it quantifies the spread or variability of data points. A standard deviation of zero would imply that all data points are identical, which is not the case in a normal distribution.
Key Learning Point
In a normal distribution, the majority of data points are concentrated around the mean, and the distribution is symmetrical and bell-shaped. It is characterized by low variability near the mean and higher variability as data points move further from the mean. The standard deviation measures the extent of this variability, and the median is equal to the mean in a perfect normal distribution.
