Homework 3: Statistical Applications Problem 1. (20 points, 10 points each): Probability and Statistics a. A process is developed to manufacture glass beakers. The beakers are made to have a mean inside diameter of 7.50 cm. To measure the volume, and a graticule line is etched to indicate the height of the solution contained, and hence the volume (Note that V = π d 2 h/ 4 and 1 mL = 1 cm 3 ). A nominal height of h = 11.32 cm corresponds to a measured volume of 500 ml . There are variations in both diameter and the height of the gradicule mark in the manufacturing process. Suppose that the diameter has a standard deviation of the diameter of σ d = 0.2 cm, and a standard deviation of the height is h = 0.1 cm . Calculate the standard deviation of the volume of the beaker. b. A set of 10 8 ft long 2 in. x 4 in. pine boards are laid end-to-end on a flat surface. If each board has a length variation of l = 0.5 in., what is the likelihood that the set of boards will exceed a total length of
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