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 endtoend 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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 Spring '09
 FRAZIER
 Statistics, Standard Deviation, Manufacturing process, power supply, nominal mean value

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