A machine manufactures cubes with a side length which varies uniformly over the interval [0.2, 0.3] in millimeters. For the following problems, make sure you use the correct units. (Assume the sides of the base and the height is all the same.)
a. What is the expected side length?
b. What is the standard deviation of the side length?
c. What is the expected area of one of the square bases?
d. What is the standard deviation of one of the square bases?
e. What is the expected volume of one of the cubes?
f. What is the standard deviation of the volume of one of the cubes?
In the rest of the problem, assume that the cost to make the cubes is 12 cents per cubic millimeter and 6 cents for the general cost (labor, electricity, etc.) per cube.
g. What is the expected cost for making 1 cube?
h. What is the variance in the cost for making 1 cube?
i. What is the expected cost for making 10 cubes?
j. What is the variance in the cost for making 10 cubes?