February 28, 2011
MATH 260
HOMEWORK
# 2
(Due March 8, 2011, Tuesday)
(Please submit your solutions to my office by 5:00 p.m, latest)
1.
A machine in a heavyequipment factory produces steel rods of length Y, where Y
is a normally distributed random variable with
μ
= 6 inches and
σ
2
= 0.2. The cost
C (in dollars) of repairing a rod that is not exactly 6 inches in length is
C = 4( Y –
μ
)
2
. If 50 rods with independent lengths are produced in a given day,
approximate the probability that total cost for repairs exceeds 48 dollars. (Note
that
)
(
~
2
1
2
n
Z
n
i
i
χ
∑
=
. Since
)
(
2
n
is actually sum of random variables by C.L.T,
for large n,
)
(
2
n
is approximately normally distributed. Use this fact to solve the
problem.)
2.
Civil engineers believe that W, the amount of weight (in units of 1000 pounds)
that a certain span of a bridge can withstand without structural damage resulting,
is normally distributed with mean 400 and standard deviation 40. Suppose that
weight (again, in units of 1000 pounds) of a car is a random variable with mean 3
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 Spring '11
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 Math, Standard Deviation

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