ISE 261
HOMEWORK SIX
Due Date: Bring to Final
1. A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction
motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load
loss is normally distributed with σ = 3.2. Provide a 95% CI for μ when n = 16 and x-bar = 58.4.
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2. Considering the information provided in problem #1, how large must n be if the width of the
99% interval for μ is to be 1.0?
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3. On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing
bar is known to be normally distributed with σ = 96. The composition of the bar has been
slightly modified, but the modification is not believed to have affected either the normality or
the value of σ. Assuming this to be the case, if a sample of 16 modified bars resulted in a
sample average yield point of 8,400 lb., provide the 90% CI for the true average yield point of
the modified bar.
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4. A random sample of 100 lighting flashes in a certain region resulted in a sample average
radar echo duration of 0.84 sec and a sample standard deviation of 0.30 sec (“Lighting Strikes
to an Airplane in a Thunderstorm,” Journal of Aircraft, 1984). Calculate a
99% (two-sided) confidence interval for the true average echo duration μ.
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5. Suppose a PC manufacturer wants to evaluate the performance of its hard disk memory
system. One measure of performance is the average time between failures of the disk drive. To
estimate this value, a quality control engineer recorded the time between failures for a random
sample of 49 disk-drive failures. A summary of the sample statistics was that x-bar = 1,710.005
hours and with sample standard deviation s = 217 hours. Estimate the true mean time between
failures with a 90% CI.
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6. The Geothermal Loop Experimental Facility, located in the Salton Sea in southern California,
is a U.S. Department of Energy operation for studying the feasibility of generating electricity
from the hot, highly saline water of the Salton Sea. Operating experience has shown that these
brines leave silica scale deposits on metallic plant piping, causing excessive plant outages.
Researchers have found that scaling can be reduced somewhat by adding chemical solutions to
the brine. In one screening experiment, each of five antiscalants was added to an aliquot of
brine, and the solutions were filtered. A silica determination (parts per million of silicon
dioxide) was made on each filtered sample after a holding time of 24 hours, with the results
shown below. Estimate the mean amount of silicon dioxide present in the five antiscalant
solutions. Use a 99% confidence interval. Empirical studies indicate that the amount of silicon
dioxide present follows approximately a normal distribution.
Silica Measurements: 229
Ans:
255
280
203
229
7. An article in the Journal of Engineering Manufacture, 2002, reports that in a sample of 64
micro-drills drilling a low-carbon alloy steel, the average lifetime (expressed as the number of
holes drilled before failure) was 12.8992 with a standard deviation of 7.84 holes. Find a 95%
confidence interval for the mean lifetime of micro-drills under these conditions.
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8. Based on the micro-drill lifetime data presented in problem #7, an materials engineer
reported a confidence interval of (10.3757, 15.4227); however, the engineer neglected to
specify the confidence level. What is the level of this confidence interval?
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9. An article in Ozone Science and Engineering, 2002, presents chemical analyses of runoff
water from sawmills in British Columbia. Included were measurements of pH for six water
specimens: 5.9, 5.0, 6.5, 5.6, 5.9, 6.5. Assuming these to be a random sample of water
specimens from an approximately normal population, find a 95% confidence interval for the
mean pH.
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10. The amount of lateral expansion (mils) was determined for a sample of n = 17 pulsed–
power gas metal are welds used in LNG ship containment tanks. The resulting sample standard
deviation was s = 2.3415 mils. Assuming normally, derive a 95% CI for σ2.
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11. The results of a Wagner turbidity test performed on 15 samples of standard Ottawa testing
sand (in microamperes) are shown below. Calculate an lower confidence bound with confidence
level 95% for the population standard deviation of turbidity. Assume the distribution is normal.
Test results:
26.7 25.8 24.0 24.9 26.4 25.9 24.4 21.7 24.1 25.9
27.3 26.9 27.3 24.8 23.6
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THE END