Final answer:
The student's question is about a continuous random variable with a specified probability density function, which is used to calculate probabilities over intervals, not at specific points.
Step-by-step explanation:
The student's question pertains to a continuous random variable (RV) and its probability density function (pdf). The given function f(x) = 0.09375(4 − x^2) for −2 ≤ x ≤ 2 represents the pdf for the error involved in making a certain measurement. The function is defined only in the interval from −2 to 2, and it is zero otherwise. This is a specific example of a pdf used to calculate probabilities for continuous outcomes, and it is different from a uniform distribution, which features equally likely outcomes and has a rectangular shape on a graph.
To find probabilities for particular intervals using the given pdf, one would integrate f(x) over the desired interval. Because the pdf gives the densities and not the probabilities for specific points, the probability that the random variable takes on any single value is zero (Ø), which is a characteristic of continuous random variables. For instance, P(x = c) = 0 for any value c.