1.  The four sides of a picture frame consist of two pieces selected from a population whose mean length is 30 cm with standard deviation 0.1 cm, and two pieces selected from a population whose mean length is 45 cm with standard deviation 0.3 cm

a.  Find the mean perimeter.

b.  Assuming the four pieces are chosen independently, find the standard deviation of the perimeter.

2.   A gas station earns $2.60 in revenue for each gallon of regular gas it sells, $2.75 for each gallon of midgrade gas, and $2.90 for each gallon of premium gas. Let X1 , X2 , and X3 denote the numbers of gallons of regular, midgrade, and premium gasoline sold in a day. Assume that X1 , X2 , and X3 have means μ1 = 1500, μ2 = 500, and μ3 = 300, and standard deviations σ1 = 180, σ2 = 90, and σ3 = 40, respectively.

a.  Find the mean daily revenue.

b.  Assuming X1 , X2 , and X3 to be independent, find the standard deviation of the daily revenue.