3 The graph of the probability density function of a random variable \(X\) is symmetrical about the line \(x = 4\). Given that \(\mathrm { P } ( X < 5 ) = \frac { 20 } { 27 }\), find \(\mathrm { P } ( 3 < X < 5 )\).
4100 randomly chosen adults each throw a ball once. The length, \(l\) metres, of each throw is recorded. The results are summarised below. $$n = 100 \quad \Sigma l = 3820 \quad \Sigma l ^ { 2 } = 182200$$ Calculate a \(94 \%\) confidence interval for the population mean length of throws by adults.