Yes, your explanation is correct, and is the "proper" interpretation
of a CI.
BUT, suppose you perform the experiment once, and calculate
a 95% CI for mu to be (3.5, 7.1). It is NOT correct to assert that
there is a 95% probability that mu lies in THIS interval. What you can say is
that THIS interval was calculated using a method that gives the
correct result 95% of the time.
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