Final answer:
True. In a continuous distribution, the probability of a specific value is zero because the probability is defined by the area under the curve at that value, and a point has no area. Probabilities are instead calculated for ranges of values.
Step-by-step explanation:
True. For a continuous distribution, the exact probability of a particular value is indeed zero. This is because a continuous random variable takes an infinite number of possible values within a range, and the probability of the variable taking on any single value is mathematically equivalent to the area under the probability curve at that point. As a single point has no area, the probability is zero.
Instead of seeking the probability of a precise value, we look at the probability that a continuous random variable falls within an interval, which is represented as P(c < x < d) or P(c ≤ x ≤ d), where c and d are numbers defining the range. To calculate this probability, we generally use the area under the curve of a probability density function. This requires calculus, specifically integral calculus, but in various educational contexts, this might be simplified using geometry, technology, or provided formulas.