Final answer:
To find P(2.5 < x < 7.5) for the given function, we need to calculate the definite integral of f(x) over the interval [2.5, 7.5].
Step-by-step explanation:
The given function is defined piecewise as follows:
f(x) = 0 if x ≤ 0
f(x) = 7 - x if 1 < x < 8
To find P(2.5 < x < 7.5), we need to find the area under the graph of f(x) between x = 2.5 and x = 7.5. This can be done by calculating the definite integral of f(x) with respect to x over the interval [2.5, 7.5].
P(2.5 < x < 7.5) = ∫[2.5, 7.5] (7 - x) dx