A Single Population Mean using the Student t Distribution · Exercise 16

The data in are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag.
$$\begin{array}{cc}\text{X}& \text{Freq.}\\ \text{1}& \text{1}\\ \text{2}& \text{7}\\ \text{3}& \text{18}\\ \text{4}& \text{7}\\ \text{5}& \text{6}\end{array}$$

As a result of your answer to, state the exact distribution to use when calculating the confidence interval.

OpenStax, Introductory Statistics 2e · §8.2 A Single Population Mean using the Student t Distribution · Exercise 16