A company assembles a product that consists of three independent components, C, R, and Z, each of which is manufactured by two suppliers, I and II. The dimensions of each component follow a normal probability distribution. A product functions satisfactorily if and only if dimensions of all three components are within their respective specification limits. The company purchases the same number of components from the two suppliers. It is equally likely that a component in a product is from either supplier I or II. The dimensions of components C and R manufactured by supplier I are within the specification limits at three standard deviations on either side of the mean. The dimensions of component Z manufactured by supplier I are within the specification limits at four standard deviations on either side of the mean. The dimensions of component R manufactured by supplier II are within the specification limits at two standard deviations on either side of the mean. The dimensions of components C and Z manufactured by supplier II are within the specification limits at four standard deviations on either side of the mean. What is the probability that a product assembled by the company functions satisfactorily?