Telephone calls arrive at a call centre randomly, at an average rate of 1.7 per minute. After the call centre was closed for a week, in a random sample of 10 minutes there were 25 calls to the call centre.
Carry out a suitable test to determine whether or not there is evidence that the rate of calls arriving at the call centre has changed.
Use a \(5 \%\) level of significance and state your hypotheses clearly.
Only 1.2\% of the calls to the call centre last longer than 8 minutes.
One day Tiang has 70 calls.
Find the probability that out of these 70 calls Tiang has more than 2 calls lasting longer than 8 minutes.
The call centre records show that \(95 \%\) of days have at least one call lasting longer than 30 minutes.
On Wednesday 900 calls arrived at the call centre and none of them lasted longer than 30 minutes.
Use a Poisson approximation to estimate the proportion of calls arriving at the call centre that last longer than 30 minutes.