2 The number of computers, \(A\), bought during one day from the Amplebuy computer store can be modelled by a Poisson distribution with a mean of 3.5. The number of computers, \(B\), bought during one day from the Bestbuy computer store can be modelled by a Poisson distribution with a mean of 5.0 .

1. 1. Calculate \(\mathrm { P } ( A = 4 )\).
   2. Determine \(\mathrm { P } ( B \leqslant 6 )\).
   3. Find the probability that a total of fewer than 10 computers is bought from these two stores on one particular day.
2. Calculate the probability that a total of fewer than 10 computers is bought from these two stores on at least 4 out of 5 consecutive days.
3. The numbers of computers bought from the Choicebuy computer store over a 10-day period are recorded as $$\begin{array} { l l l l l l l l l l } 8 & 12 & 6 & 6 & 9 & 15 & 10 & 8 & 6 & 12 \end{array}$$
   1. Calculate the mean and variance of these data.
   2. State, giving a reason based on your results in part (c)(i), whether or not a Poisson distribution provides a suitable model for these data.