7. (2 points each) In a certain town, 78% of the population favors a warrant article reducing the 100 ft setback to 50 ft. A random sample of 40 people in the population are surveyed. a. Determine the probability that at least 22 favor the policy. b. Determine the probability that at most 20 favor the policy. c. Determine the probability that more than 30 favor the policy. d. Determine the probability that fewer than 25 favor the policy. e. Determine the probability that exactly 25 favor the policy. 5. (2 points each) 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. a. Determine the probability that the mean extra length for the 30 boards is less than 2 inches. b. Determine the probability that the mean extra length for the 30 boards is more than 3.5 inches. c. Determine the probability that the mean extra length for the 30 boards is between 2.5" and 4". d. Determine the probability that the total extra length for the 30 boards is less than 80 inches. e. Determine the probability that the total extra length for the 30 boards is more than 105 inches. f. Determine the 80th percentile for the total extra length for the 30 boards. g. Determine the first quartile for the total extra length for the 30 boards.