USE SALT a) What is the probability that defect length is at most 20 mm? Less than 20 mm? (Round your answers to four decimal places.) at most 20mm less than 20mm .14007 .14007 X X ) What is the 75th percentile of the defect length distribution-that is, the value that separates the smallest 75% of all lengths from the largest 25% ? (Round your four decimal places.) 33.293 mm :) What is the 15th percentile of the defect length distribution? (Round your answer to four decimal places.) 19.863 X mm d) What values separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10%? (Round your answers to four decimal places.) smallest 10% 17.88 mm largest 10% 37.472 x mm
USE SALT a) What is the probability that defect length is at most 20 mm? Less than 20 mm? (Round your answers to four decimal places.) at most 20mm less than 20mm .14007 .14007 X X ) What is the 75th percentile of the defect length distribution-that is, the value that separates the smallest 75% of all lengths from the largest 25% ? (Round your four decimal places.) 33.293 mm :) What is the 15th percentile of the defect length distribution? (Round your answer to four decimal places.) 19.863 X mm d) What values separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10%? (Round your answers to four decimal places.) smallest 10% 17.88 mm largest 10% 37.472 x mm
USE SALT a) What is the probability that defect length is at most 20 mm? Less than 20 mm? (Round your answers to four decimal places.) at most 20mm less than 20mm .14007 .14007 X X ) What is the 75th percentile of the defect length distribution-that is, the value that separates the smallest 75% of all lengths from the largest 25% ? (Round your four decimal places.) 33.293 mm :) What is the 15th percentile of the defect length distribution? (Round your answer to four decimal places.) 19.863 X mm d) What values separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10%? (Round your answers to four decimal places.) smallest 10% 17.88 mm largest 10% 37.472 x mm
The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 28 mm and standard deviation 7.9 mm.
Transcribed Image Text:The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 28 mm and standard deviation 7.9 mm.
USE SALT
(a) What is the probability that defect length is at most 20 mm? Less than 20 mm? (Round your answers to four decimal places.)
at most 20mm
.14007
X
less than 20mm
.14007
X
(b) What is the 75th percentile of the defect length distribution—that is, the value that separates the smallest 75% of all lengths from the largest 25%? (Round your answer to
four decimal places.)
33.293
mm
(c) What is the 15th percentile of the defect length distribution? (Round your answer to four decimal places.)
19.863
X mm
(d) What values separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10%? (Round your answers to four decimal places.)
smallest 10%
mm
largest 10%
X mm
17.88
37.472
You may need to use the appropriate table in the Appendix of Tables to answer this question.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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