Final answer:
For a uniform probability function f(x) over the interval [0, 12], the probability P(0 < x < 12) is 1, indicating that the event x falling within this range is certain.
Step-by-step explanation:
The student seems to be working on a problem involving probability functions and perhaps is looking for the probability P(0 < x < 12) for a continuous probability function f(x). The statement 'f(x), a continuous probability function, is equal to 12, and the function is restricted to 0 ≤ x ≤ 12' indicates that f(x) is likely a uniform distribution over the interval [0, 12]. If f(x) is indeed a uniform distribution, then the probability density function would be a constant over the allowed range. Since the total area under a probability density function over its entire domain equals 1, and considering that the function f(x) is nonzero and constant between 0 and 12, we would divide 1 by the length of the interval, which is 12, to find that constant value.
The constant value of the probability density function f(x) would be 1/12. Therefore, the probability P(0 < x < 12) would simply be the area under the curve between 0 and 12, which is the product of the constance density 1/12 and the interval length, which is 12. Hence, P(0 < x < 12) = 1/12 × 12 = 1. This means that the total probability over the interval (0, 12) is 100% or certain, which makes sense for a continuous probability function over its entire domain where it is nonzero.