Question

The total area under the probability density curve of any continuous distribution is 1.0.
a. true
b. false

Answer 1

It is true by definition of a probability curve.

Area under the domain of ALL continuous probability curves is 1.0.

If the area under a curve's domain does not add up to 1.0, it is not a probability curve.  (contrapositive of the same statement!)

Answer 2

It is true by definition of probability curve