Answered: (a) A structure consists of 100 column…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....

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Question

(a) A structure consists of 100 column footings. Suppose the settlement of each
footing is exponentially distributed with a mean of 2 inches and the settlements
between footings are statistically independent. What is the probability that the
maximum settlement Smax among the 100 footings will not exceed 5.0 inches?
Compare this exact probability with the answer obtained assuming an appropriate
asymptotic distribution for Smax

b. What is the probability that the minimum settlement Smax is at least 0.5 inches?

c. Determine the mean and coefficient of
variation of the maximum differential settlement delta(max) defined as (Smax-Smin)

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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