You would like to construct a $95\%$ confidence interval to estimate today's population mean temperature, so you make a series of measurements $($a random

sample$)$ throughout the day. The mean of these measurements is $62\mathrm{.}5$ degrees Fahrenheit, and their standard deviation is $4\mathrm{.}0$ degrees Fahrenheit.

$($a$)$ What is the best point estimate, based on the sample, to use for the population mean?

$$ degrees

$($b$)$ For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value

for the $95\%$ confidence interval for the population mean.

$($In the table, $Z$ refers to a standard normal distribution, and $t$ refers to a $t$ distribution.