a rough lumber mill cuts pine and hemlock lumber to order. rough lumber is not cut to exact dimensions. it is always cut longer than specified. thus, if you buy an 8-foot board it will be longer than 8 feet. the boards will not be smooth, thus, it will be a rough surface. the boards vary in extra length between one and five inches. the extra lengths are a uniform distribution. you take a sample of 30 boards from the lumber mill. determine the probability that the mean extra length for the 30 boards is less than 2 inches