Problem

A scientist is investigating the lengths of the leaves of a certain type of plant. The scientist assumes that the lengths of the leaves of this type of plant are normally distributed. He measures the lengths, $x$ cm, of the leaves of a random sample of 8 plants of this type. His results are as follows.

$$\begin{gathered} 3.5 \qquad 4.2 \qquad 3.8 \qquad 5.2 \\ 2.9 \qquad 3.7 \qquad 4.1 \qquad 3.2 \end{gathered}$$

Find a 90% confidence interval for the population mean length of leaves of this type of plant.