2-4. The outcome from throwing a single, true, six-sided die is a random variable. Its mean is equal to 3.50, and the standard deviation is equal to 1.71.
(1) Assume
where X1 and X2 represent
two dice. Based
on the principel of linear operator, calculate 
and
.(2) Assume
, calculate and .
Chapter 3. Statistical Process Control
3.9 Assignment Problems ( Page 3-64, 2-67 )
3-1. You need to make some decisions regrding the procurement of bolts
from three different suppliers. You have requested that the shank diameter
(above the thread) have specifications of 1.500±0.009 inches. The SPC
studies done by the suppliers have indicated that their processes are
behaving consistently in statistical control with the following process
parameters. The individual measurements follow the normal
distribution.
Supplier 1: 
= 1.500 inches,
= 0.003 inch.
Supplier 2: = 1.500 inches,
= 0.0022 inch.
Supplier 3: = 1.4950 inches,
= 0.0015 inch.
Which supplier would you purchase from? Why? Explain your locig and show
calculations and graphical evidence to back it up.
3-2. the specifications of the thickness of a low-alloy steel gear blank
are 0.3000 ± 0.0015 centimeter.
a. If it is desired that the value of 
be at least
1.25, what would be the minimum of a
centered
process?
b. If the specifications change to 
centimeter,
what would be the minimum for a
centered
process?
3-3. A desinger has specified a tolerance: 
. A
production engineer has adjusted the machine to the following
configuration:
limit principle to
determine the
precentage of non-conforming products at the present seeting.