Final answer:
When forming confidence intervals for a random sample from a normal distribution, the choice between using standard normal values (z) or the t-distribution values (t) depends on the sample size and whether the population standard deviation is known or unknown.
Step-by-step explanation:
When forming a confidence interval for a random sample from a normal distribution, we can compare the standard normal values (z) with the corresponding values of the t-distribution (t). The choice between z and t depends on the sample size and whether the population standard deviation is known or unknown.
(a) For a % confidence interval, z should be used if the sample size is large (typically n > 30) or if the population standard deviation is known. t should be used if the sample size is small (typically n < 30) and the population standard deviation is unknown.
(b) and (c) are incomplete in the question. Please provide the confidence level (in decimal form) and the corresponding degrees of freedom (df) for a complete answer.