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 R.V. 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