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.
Let 
denote the lengths of the pieces chosen from the population with mean 30 and standard deviation 0.1, and let 
denote the lengths of the pieces chosen from the population with mean 45 and
standard deviation 0.3.
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