Consider a major forest products company in the United States. In addition to timberlands, the company owns and operates numerous manufacturing plants that make lumber and paper products. At one of their plywood plants, the operations manager has been struggling to make sure that the plywood thickness meets quality standards. Specifically, all sheets of their 1 / 2-inch plywood must fall within the range 0.492 to 0.508 inches in thickness. Studies have shown that the current process produces plywood that has thicknesses that are normally distributed with a mean of 0.507 inches and a standard deviation equal to 0.005 inches. Complete parts a and b below. . . . a. Use technology to determine the proportion of plywood sheets that will meet quality specifications (0.492 to 0.508), given how the current process is performing. The proportion is (Round to four decimal places as needed.)Suppose a random variable, x, has a uniform distribution with a = 8 and b = 18. a. Calculate P(10.5 s x s 14). b. Determine P(x > 13). c. Compute the mean, p, and the standard deviation, 6, of this random variable. d. Determine the probability that x is in the interval (p j: 30'). E) a. P(10.5 s x S 14) = .35 (Simplify your answer.) b. P(x > 13) = .5 (Simplify your answer.) c. p = 13 (Simplify your answer.) 0' = 2.887 (Round to three decimal places as needed.) d. P(p. - 30 5x5 p + 30) = :| (Round to three decimal places as needed.)