- In a factory, a machine is used to fill bags of rice. The weights of bags of rice are modelled using a normal distribution with mean 250 g .
Only \(1 \%\) of the bags of rice weigh more than 256 g .
- Write down the percentage of bags of rice with weights between 244 g and 256 g .
- Find the standard deviation of the weights of the bags of rice.
An inspection consists of selecting a bag of rice at random and checking if its weight is within 4 g of the mean. If the weight is more than 4 g away from the mean, then a second bag of rice is selected at random and checked. If the weight of each of the 2 bags of rice is more than 4 g away from the mean, then the machine is shut down.
- Find the probability that the machine is shut down following an inspection.