Final answer:
The function f(x) is greater than or equal to 0 for the entire interval from x = 0 to x = 20, inclusive, because it is graphed as a horizontal line at f(x) = 10. For the continuous probability distribution, the probabilities of a single point are 0, and the probability for an interval is calculated as the area under the curve within that interval.
Step-by-step explanation:
To determine all intervals on which f(x) is greater than or equal to 0, we need to look at the description of the function. We are considering the function f(x) for 0 ≤ x ≤ 20, where x is a real number. The graph of f(x) is described as a horizontal line at f(x) = 10. Since a horizontal line at f(x) = 10 indicates that the function's value is consistently 10 for all x within the interval, f(x) ≥ 0 throughout the entire interval from x = 0 to x = 20, inclusive.
To answer the probability questions based on the continuous probability distribution, one would need to calculate the areas under the density function within the specified intervals. However, for a continuous distribution:
- P(x > 15), would be 0 since the function is limited to 0 ≤ x ≤ 15.
- P(x = 7) or any specific value is 0, as a continuous distribution has a probability of 0 at any single point.
- P(x < 0) is 0 when the function is restricted to 0 ≤ x ≤ 5.