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 disks.