Please answer the question in full providing any relevant equations or diagrams used to come to a final answer.
a) In a pavement study the diameter of the aggregate stones is found to be normally distributed with a mean of 4 cm and a standard deviation of 0.5 cm. Say this distribution is denoted by Random Variable X, show the equation convert X to a standard normal distribution.
b) For a standard normal distribution, separately find z such that
i) the area to the right of z is 0.1949
ii) the area to the left of z is 0.0655
iii) the area between -0.13 and z is 0.3311