Final answer:
For a horizontal line f(x) such as f(x) = 1, f(x) will be greater than 0 for the entire given interval from 0 to 20. In a continuous probability distribution, probabilities of x equaling a single value are 0.
Step-by-step explanation:
Selecting the Interval Where f(x) > 0
To answer the question of selecting the interval where f(x) > 0, we first need to know the nature of the function f(x). If f(x) is a horizontal line, its value is the same for all x within its domain.
Based on the information provided, it seems that part of the function is a constant value. For example, if f(x) = \frac{20}{20} for 0 ≤ x ≤ 20, the function value is 1, and since a constant function that equals 1 is always positive, f(x) is greater than 0 for the entire interval from 0 to 20, inclusive.
However, when it comes to probability distributions like the one mentioned in Figure 5.41, scenarios such as P(x > 15), P(x = 7), and P(x = 10) depend on the specific definitions of the probability functions provided.
For continuous probability distributions, the probability that x equals any single value is 0, so P(x = 7) and P(x = 10) would be 0. The probability of x being greater than a certain value would be calculated using the integral of the probability density function over the interval of interest.