3 Fiona is studying the heights of corn plants on a farm. She measures the height, \(x \mathrm {~cm}\), of a random sample of 200 corn plants on the farm.
The summarised results are as follows: $$\sum x = 60255 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 995$$ Calculate a \(96 \%\) confidence interval for the population mean of heights of corn plants on the farm, giving your values to one decimal place.
\begin{center} \begin{tabular}{|l|l|l|l|} \hline \multicolumn{3}{|l|}{\begin{tabular}{l} \(\begin{aligned} & 4 \text { The continuous random variable } X \text { has probability density fu }
& \qquad f ( x ) = \begin{cases} \frac { 4 } { 99 } \left( 12 x - x ^ { 2 } - x ^ { 3 } \right) & 0 \leq x \leq 3
0 & \text { otherwise } \end{cases} \end{aligned}\)