Let f and g be linear functions with equations f(x) = m1x + b1 and g(x) = m2x + b2.
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No. It is not that the probability that 
is in the interval is 0.95 rather we are 95% confident that the true mean of the population will be in the stated interval.
Confidence interval does not specify the probability of the occurrence of a population mean in an interval, rather it specifies the level of confidence on the interval of occurrence of the population mean.
Confidence interval does not specify the probability of the occurrence of a population mean in an interval, rather it specifies the level of confidence on the interval of occurrence of the population mean.