Assume that a random variable is normally distributed with a mean of 1,400 and a variance of 304. Complete parts a through c below. E) a. What is the probability that a randomly selected value will be greater than 1,420? The probability is (Round to four decimal places as needed.) 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. Specically, 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 specications (0.492 to 0.508), given how the current process is performing. The proportion is 0.5779 . (Round to four decimal places as needed.) b. Referring to part a, suppose the manager is unhappy with the proportion of product meeting specications. Assuming that he can get the mean adjusted to 0.5 inches, what must the standard deviation be if he is going to have 95% of his product meet specications? The standard deviation must be inches. (Round to three decimal places as needed.)