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Solutions to Homework 9
5.85
Let
X
denote the amount spent for maintenance and repairs in a certain company in
the next week, then
X
has an approximately normal distribution with mean of 600 and
standard deviation of 40. Hence, the probability that actual costs will exceed the
budgeted amount is
600
700 600
(
700)
(
)
40
40
(
2.5)
0.0062
X
P X
P
P Z
Z
has a standard normal distribution.
5.93
Let
X
denote the resistance of the certain type of capacitor,
X
has a normal
distribution with mean of 800 and standard deviation of 200, then
a.The proportion of capacitors which will meet this specification is
900 800
800
1000 800
(900
1000)
200
200
200
(0.5
1)
(0
1)
(0
0.5)
0.3413 0.1915
X
P
X
P
P
Z
P
Z
P
Z
0.1498
b. Define events
A: the first capacitor chosen satisfy the specifications
B: the second capacitor chosen satisfy the specificaions
Because the two capacitors are randomly chosen, then

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