Suppose we repeat an experiment identically and independently 100 times. Each time we construct a 99% conﬁdence interval for $\mu$ via the t-distribution. Let X = the number of times the conﬁdence interval fails to contain the true value of $\mu$. The distribution of X is:
Normal with $\mu=0$ and $\sigma^2 = 1$, is this correct? Since in Normal, the mean should be zero and the variance is always one.
Since this is a t-distribution, it should be Normal. I thought another answer might suit it being Normal with $\mu = 99$ and $\sigma^2 = 0.99$
Could someone explain which one could be correct, if correct at all?