2 Emilia runs an online perfume business from home. She believes that she receives more orders on Mondays than on Fridays. She checked this during a period of 26 weeks and found that she received a total of 507 orders on the Mondays and a total of 416 orders on the Fridays. The daily numbers of orders that Emilia receives may be modelled by independent Poisson distributions with means \(\lambda _ { \mathrm { M } }\) for Mondays and \(\lambda _ { \mathrm { F } }\) for Fridays.

1. Construct an approximate \(99 \%\) confidence interval for \(\lambda _ { \mathrm { M } } - \lambda _ { \mathrm { F } }\).
2. Hence comment on Emilia's belief.