(a) Give a brief outline describing how confidence intervals for means use the normal distribution or Student's t distribution in their basic construction.

(a) Give a brief outline describing how confidence intervals for means use the normal distribution or Student's t distribution in their basic construction.
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The normal distribution is used for confidence interval in their basic construction when the population standard deviation $\left(\sigma \right)$ is known.
Let x be a random variable. If it is assumed that x has a normal distribution, then any sample size will work. If it is not assumed that x has normal distribution, then the sample size should be greater 30.
For constructing confidence interval, sample mean $\left(\stackrel{―}{x}\right)$, population standard deviation $\left(\sigma \right)$, sample size n, and critical z value are used.
The confidence interval for means at a is as follows:
$CI=\left\{\stackrel{―}{x}±\frac{{z}_{a}}{2}\ast \frac{\sigma }{\sqrt{n}}\right\}$