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Because P(x = c) is zero for a continuous variable, P(c < x < d) and P(c <= x <= d) are:
AEqual to each other
BDifferent by one half
CDifferent by exactly one
DImpossible to compare
Answer & Solution
Correct answer: A. Equal to each other
1. Endpoints contribute no area under a density curve.
2. The probability that x takes on any single individual value is zero.
3. Adding the two endpoints therefore adds zero probability.
4. P(c < x < d) is the area to the right of c and left of d.
5. So the strict and non-strict interval probabilities are equal to each other.
_Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 5 'Continuous Random Variables', sections 5.1-5.3_
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