A company which manufactures computer disks has a good reputation for the reliability of the disks that it produces. It is known that only 1 per cent of the disks which are manufactured by this company are faulty.
The disks are packed in boxes of 500.
a) i ) Write down the probability distribution for X, the number of faulty disks in a box of 500 disks.
ii ) Calculate the probability that there is exactly one faulty disk in a randomly selected box of 500 disks.
b) Find values for the mean and variance of X.
c) Using a distribution approximation, calculate the probability that there are more than 10 faulty disks in a box of 500 disk