Final answer:
The student's question involves finding the probability associated with a given range for a uniform probability distribution, f(x), which is a constant function. The probability is determined by the area under the curve between two points on the x-axis for this constant function.
Step-by-step explanation:
From the information provided, it seems that the question is asking about a probability function f(x) which is a constant value over a specific interval. When a function such as f(x) = 14 is a constant over an interval, it represents a uniform probability distribution in the context of probability theory. In this case, over the interval [-12, -7], this means that every value of x within this interval is equally likely.
For the given function f(x) = 14 within an interval, f(x) does not represent a probability unless it is normalized. For a continuous probability function to be valid, the total area under the curve must equal 1. Assuming the normalization has occurred, to find the probability that x is between any two values, one must calculate the area under the function between those two points. Since this function is constant, the probability P(a < x < b) over the interval [a, b] would be represented by the area of the rectangle with height equal to the probability density (in this case, the constant value of the function) and width equal to (b-a).