The permeability of a membrane used as a moisture barrier in a biological application depends on the thickness of three integrated layers. Layers 1, 2, and 3 are normally distributed with means of 0.5, 1, and 1.5 millimeters, respectively. The standard deviations of layer thickness are 0.1, 0.2, and 0.3, respectively. Also, the correlation between layers 1 and 2 is 0.7. between layers 2 and 3 is 0.5, and between layers 1 and 3 is 0.3. (a) Determine the mean and variance of the total thickness of the three layers. Mean 0.246 mm Variance = i 0.0012 mm2 (b) What is the probability that the total thickness is less than 1.5 millimeters? Round your answer to four decimal places (e.g. 98.7654). 0.346