3 A supermarket sells cashew nuts in three different sizes of bag: small, medium and large. The weights in grams of the nuts in each type of bag are modelled by independent Normal distributions as shown in Table 3.
\begin{table}[h]
| Bag size | Mean | Standard deviation |
| Small | 51.5 | 1.1 |
| Medium | 100.7 | 1.6 |
| Large | 201.3 | 1.7 |
\captionsetup{labelformat=empty}
\caption{Table 3}
\end{table}
- Find the probability that the mean weight of two randomly selected large bags is at least 200 g .
- Find the probability that the total weight of eight randomly selected small bags is greater than the total weight of two randomly selected medium bags and one randomly selected large bag.