Final answer:
In a symmetric density curve, it is not true that the mean is greater than the median, as both are situated at the center and are equal. The area under the curve is indeed 1, and the curve being symmetric means it is not skewed.
the correct statement is: a) The area under the curve is 1.
Step-by-step explanation:
For the density curve in question, several characteristics can be determined. According to the principles of density curves and the properties of normal distributions, we can assess the given options.
Firstly, it is a fundamental property of a density curve that the area under the curve is 1, as this area represents the entirety of the probability distribution for that variable. Secondly, if the curve is symmetric, then the mean, median, and mode are all equal and situated at the center of the distribution. Hence, for a symmetric curve, it is not true that the mean is greater than the median.
Thirdly, skewness refers to the direction of the tail of the curve; if the tail extends more to the left, it is negatively skewed, and if it extends to the right, it is positively skewed.
Given this information, if the student has indicated that the curve is symmetric, option c) stating 'The mean is greater than the median' would not be true. In a symmetric distribution, the mean and median are the same, located at the center peak of the distribution.