- It is suggested that the delay, in hours, of certain flights from a particular country may be modelled by the continuous random variable, \(T\), with probability density function
$$f ( t ) = \left\{ \begin{array} { c l }
\frac { 2 } { 25 } t & 0 \leqslant t < 5
0 & \text { otherwise }
\end{array} \right.$$
- Show that for \(0 \leqslant a \leqslant 4\)
$$P ( a \leqslant T < a + 1 ) = \frac { 1 } { 25 } ( 2 a + 1 )$$
A random sample of 150 of these flights is taken. The delays are summarised in the table below.
| Delay ( \(\boldsymbol { t }\) hours) | Frequency |
| \(0 \leqslant t < 1\) | 10 |
| \(1 \leqslant t < 2\) | 13 |
| \(2 \leqslant t < 3\) | 24 |
| \(3 \leqslant t < 4\) | 35 |
| \(4 \leqslant t < 5\) | 68 |
- Test, at the \(5 \%\) significance level, whether the given probability density function is a suitable model for these delays.
You should state your hypotheses, expected frequencies, test statistic and the critical value used.