Due:
In class, Friday
February 15, 2008
Name(s)
(up to four students per homework set)
:
Section number(s)
1.
2.
3.
4.
For instructor or TA use only:
Problem
Score
Points
1
10
2
15
3
15
4
20
5
15
6
15
7
10
M E 345
Spring Semester, 2008
Homework Set # 4
Professor J. M. Cimbala
Total:
100
1
.
(10 pts)
A large manufacturing plant uses a certain brand of light bulbs that has a
mean time to failure
(MTTF) of 3600
hours with a standard deviation of 160 hours. Good lighting in the plant is critical to safety, and the plant manager
determines that no more than 10% of the bulbs should fail while being used. He institutes a policy to replace
all
the light
bulbs simultaneously according to a set schedule, rather than to replace individual bulbs as they burn out.
After how many
hours should
all
the bulbs be replaced such that no more than 10% of the bulbs will fail while being used? (You may
assume that the variations in MTTF are
random
.)
2
.
(15 pts)
A quality control engineer pulls 10 bearings at random from an assembly line, and measures the diameter of each
one. The measurements are 5.08, 5.16, 5.06, 5.04, 5.10, 5.18, 5.04, 5.06, 5.12, and 5.09 mm.
(
a
) Estimate the population mean and its confidence interval for 95% confidence level. For consistency, give your answer
to three decimal places to the right of the decimal point.
(
b
) Estimate the population standard deviation and its confidence interval for 95% confidence level. For consistency, give
your answer to three decimal places to the right of the decimal point.

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