Answer
a) t-distribution
b) z-distribution
c) not normal
d)chi-square distribution
Work Step by Step
a) The sample size is large (at least 30), hence the ditribution is rougly normal. Standard deviation is unknown hence we will have to use t-distribution to estimate $\mu$.
b)The sample size is large (at least 30), hence the ditribution is rougly normal. Standard deviation is known hence we will have to use z-distribution to estimate $\mu$.
c) The distribution is not normal, hence we cannot estimate a confidence interval.
d) The distribution is normal, hence we can use the chi-square distribution to estimate $\sigma$'s confidence interval.
