5 The number of letters per week received at home by Rosa may be modelled by a Poisson distribution with parameter 12.25.
- Using a normal approximation, estimate the probability that, during a 4 -week period, Rosa receives at home at least 42 letters but at most 54 letters.
- Rosa also receives letters at work. During a 16-week period, she receives at work a total of 248 letters.
- Assuming that the number of letters received at work by Rosa may also be modelled by a Poisson distribution, calculate a \(98 \%\) confidence interval for the average number of letters per week received at work by Rosa.
- Hence comment on Rosa's belief that she receives, on average, fewer letters at home than at work.