6. The number of toasters sold by a shop each week may be modelled by a Poisson distribution with mean 4
A random sample of 35 weeks is taken and the mean number of toasters sold per week is found.
- Write down the approximate distribution for the mean number of toasters sold per week from a random sample of 35 weeks.
The number of kettles sold by the shop each week may be modelled by a Poisson distribution with mean \(\lambda\)
A random sample of 40 weeks is taken and the mean number of kettles sold per week is found. The width of the \(99 \%\) confidence interval for \(\lambda\) is 2.6
- Find an estimate for \(\lambda\)
A second, independent random sample of 40 weeks is taken and a second \(99 \%\) confidence interval for \(\lambda\) is found.
- Find the probability that only one of these two confidence intervals contains \(\lambda\)