When explaining the meaning of a confidence interval don’t say “the probability that the parameter is in the interval is 0.95” because probability is a precious concept and this statement does not match the meaning of this term. Instead, say “We are 95% confident that the parameter is in the interval”.  Admittedly, I don’t know what people will make of the word “confident”. But I also don’t know what they will make of the word “probability”