Problem

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

$$f(t)= \begin{cases} \frac{t}{25}, & 0 \le t < 5 \\ 0, & \text{otherwise} \end{cases}$$

(a) Show that for $0 \le a \le 4$

$$P(a \le T < a+1)=\frac{1}{25}(2a+1)$$

A random sample of 150 of these flights is taken. The delays are summarised in the table below.

Delay (t hours)	Frequency
$0 \le t < 1$	10
$1 \le t < 2$	13
$2 \le t < 3$	24
$3 \le t < 4$	35
$4 \le t < 5$	68

(b) 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.