Final answer:
The distribution of heights according to the National Center for Education Statistics follows a normal distribution, characterized by a bell-shaped curve where the mean, median, and mode coincide at the peak.
Step-by-step explanation:
According to the National Center for Education Statistics, the distribution of heights follows a normal distribution. This is because human height exhibits the typical characteristics of a normal distribution with a bell-shaped curve, when considering a large sample size.
With a normal distribution, the mean, median, and mode all coincide at the peak of the bell curve. The distribution is symmetric about the mean, which acts as a line of symmetry. The standard normal distribution is a special case where the mean is zero and the standard deviation is one. The characteristics of normally distributed data are not only applicable to height but also to many human traits, like IQ scores used in psychological testing, where the mean IQ is 100 with a standard deviation of 15.
Regarding the question, the normal distribution is less reliable when the number surveyed is very small, such as 15. However, as the sample size increases, the distribution of the data is more likely to resemble a normal distribution, which is why the answer to the student's question is A) Follows a normal distribution, assuming a large sample size is surveyed.