HW #4 DUE November
5, 2003
TOPIC: STATISTICS
PROBLEMS 17, 22, 24, and 26
Pages 60-62
17. The results of a life test on
automotive catalytic converters showed that 25.0% failed within 60,000 mi of driving
and 50% failed by 90,000 mi. Assuming a normal distribution, estimate the
mileage at which 95.0% will have failed.
- As a
part of testing a newly designed energy
efficient light bulb, 200 have been subjected to a life test
simultaneously. By the end of 2000
hr, five of the 200 bulbs have failed; by the end of 3500 hr, three more
of the 200 have failed. Determine
the standard deviation and the average life of these bulbs. HINT:
If you use f(z1)=0.025 and f(z2) = 0.040,
the resulting z1 and z2 can be used for simultaneous solutions for the
standard deviation and the average.
- For a
quality control study, 500 resistors with a nominal value of 3.00 MegaOhms are taken randomly from production. Of these samples, 200 have resistances
that are equal to 2.91 MegaOhms or highter, and 100 have resistances that are 3.05 MegaOhms or higher.
Determine
a.
The mean and standard deviation
b.
What percentage of these resistors fall within the
range of 3.00 MegaOhms +/-5%
- Packaging
machinery is required to fill breakfast cereal boxes with precision. If the amount of cereal is too little,
there are legal implications. If
there is more than enough in the boxes, profits suffer. One hundred randomly selected samples
from production yielded the following information:
Minimum observed mass 453.44 g
Maximum observed mass 456.10 g
Median mass 454.80 g
Average mass 454.85 g
Standard deviation 0.3504 g
Assuming
the data are normally distributed, for a production run of 20000 boxes of
cereal determine:
a.
the number of boxes expected to contain less than
453.60 g or less;
b.
the number of boxes that will have a mass of 453.44 g
or less, and
c.
the minimum mass of 99.00% of
the production.