4 The manager of a medical centre suspects that patients using repeat prescriptions were requesting, on average, more items during 2011 than during 2010. The mean number of items on a repeat prescription during 2010 was 2.6.
An analysis of a random sample of 250 repeat prescriptions during 2011 showed a total of 688 items requested. The number of items requested on a repeat prescription may be modelled by a Poisson distribution. Use a distributional approximation to investigate, at the \(5 \%\) level of significance, the manager's suspicion.