The pressure of air (in MPa) entering a compressor is measured to be X = 8.5 ± 0.2, and the pressure of the air leaving the compressor is measured to be Y = 21.2 ± 0.3. The intermediate pressure is therefore measured to be P = √XY = 13.42. Assume that X and Y come from normal populations and are unbiased.

a. From what distributions is it appropriate to simulate values X^∗ and Y^∗?

b. Construct a normal probability plot for the values P^∗. Is it reasonable to assume that P is approximately normally distributed?