When stone benchtops are produced there are on average there are 2 blemishes in a 4 meter stone piece.

a. If the random variable X is the number of blemishes in a 4 metre slab of the material when the process is operating correctly, then identify the distribution of X and state the value/s of its parameter/s.

b. Calculate (using the appropriate statistical tables) the probability that the correctly operating process produces a 4 metre slab for domestic use with less than 2 blemishes.

c. Production is modified without loss of quality to produce 8 metre slabs for commercial purposes. Calculate (using the appropriate statistical tables) the probability of exactly five blemishes in an 8 metre slab produced when the process is operating correctly.