Final answer:
To determine the height of the density curve, one must examine the probability density of the data set, which necessitates understanding the mean and standard deviation for a normal distribution.
Step-by-step explanation:
To find the height of the density curve between 0 and 6, you must examine the probability density (option c) of the data set. The height of a point on a probability density curve represents the density of probability at that value. In other words, it encodes how likely we are to observe a value in a tiny interval around that point when randomly sampling from the distribution.
The mean or expected value (μ) of a distribution is the arithmetic average of a random variable's possible values, weighted by the probabilities of those values. The standard deviation (σ) measures the amount of variation or dispersion in a set of values. For a normal distribution, which is symmetrical and bell-shaped, both of these parameters are crucial as they define its shape and spread.
If we assume a normal distribution, the location of the mean indicates the point on the x-axis where the curve peaks, and the standard deviation dictates how spread out the curve is. The height at any given point could be calculated using the probability density function for the normal distribution, but this typically requires knowledge of these two parameters.