Final answer:
In a continuous probability distribution, P(x > 6) and P(x ≥ 6) are equivalent because the probability of a continuous random variable equaling any single value is zero.
Step-by-step explanation:
The statement that in a continuous probability distribution, there is no difference between P(x > 6) and P(x ≥ 6) is TRUE. In continuous probability distributions, the probability that X equals any single value is always zero, which means P(x = 6) = 0. Therefore, whether we are looking for the probability greater than 6 or greater than or equal to 6, the result is the same because the probability of X being exactly 6 does not add anything to the total probability. For example, if f(x) is a continuous probability density function, the total area under the curve f(x) is one, representing the maximum probability. To find probabilities, we look at the area under the curve over an interval, rather than at a specific point.
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