Quiz 2
Please put your answers in the following table.
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5 |
6 |
7 |
8 |
9 |
10 |
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1. If
X follows a normal distribution with mean 
and
standard deviation 
, which transformation changes X
to a standard normal random variable?
A) 
B)
C)
D)
2.
If 
and 
are independent and 
is a positive constant, which of the
following statement about the standard deviation is not true?
A)
B)
C)
D)
3. A bar is measured 10 times, and the measured lengths are given below.
99.8
85.0
106.5
108.5
91.2
119.3
119.3
104.5
108.9
107.1
The average of the length is
A) 90.2 mm B) 105 mm C) 95 mm C) 110.1 mm
4. For problem 3, the standard deviation of the length is
A) 10.9 mm
B) 20.1 mm
C) 5.6 mm
D) 0.8 mm
5. A rod has a
diameter D =
2.4 in. It is subjected to a shear force of 
. If
the allowable shear stress is 
, which statement is
not true? Assume that 
and 
are
independent.
( Hint: The first moment of the cross section
area at the neutral axis: 
, in which 
, and 
)
A) The shear stress follows a normal distribution.
B) The mean value of the shear stress is a linear function of that of F.
C) The standard deviation of the shear stress is a linear function of that of F.
D)
The
shear stress depends on .
6. For problem 5, what is the probability of failure of the rod?
A) 0
B)
C)
D)
7. A shaft has an
outer diameter of 32 mm and an inner diameter of 20 mm. Two torques 
and 
are
applied to the shaft. If 
and 
, which statement about the maximum shear
stress developed in the shaft is true? Assume that and are independent.
A)
follows a normal distribution.
B)
is a linear function of .
C)
is a linear function of .
D)
The
mean of is 25 MPa.
8.
For
problem 7, if the allowable shear stress is 
, , , and are independent, what is the probability
of failure of the shaft?
A)
B)
C)
D)
9. A rod is subject to two forces as shown
below. The rod is 16 in. long and its diameter is 
. The
yield strength of the rod is 
. The modulus of
elasticity follows a normal distribution 
. The forces also
follow a normal distribution 
. Which statement
about the critical buckling force 
is not true? Assume
that 
and are 
are
independent.
( Hint: the critical buckling force : 
, in which 
)
A)
follows a normal distribution.
B)
and 
are
dependent.
C)
The
mean of is 3.42 kip.
D)
The
standard deviation of is 0.41kip.
10. For problem 9, find the probability of failure of the rod caused by buckling.
A) 0.5
B)
C)
D)
