Suppose steel wires have the tensile strength represented by a normal distribution with mean value equal to 5000N and standard deviation equal to 150N. Knowing that these wires will be used in the manufacture of a steel cable to be mounted on the boom of a crane, what should be the number of wires to be used in the manufacture of this cable so that the probability of the cable breaking with a load less than 50,000N is 2%? What would be the safety factor associated with this probability of failure? Suppose the resistance of the cable is expressed by the sum of the resistance of the wires that make it up.

Suppose steel wires have the tensile strength represented by a normal distribution with mean value equal to 5000N and standard deviation equal to 150N. Knowing that these wires will be used in the manufacture of a steel cable to be mounted on the boom of a crane, what should be the number of wires to be used in the manufacture of this cable so that the probability of the cable breaking with a load less than 50,000N is 2%? What would be the safety factor associated with this probability of failure? Suppose the resistance of the cable is expressed by the sum of the resistance of the wires that make it up.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 4CYU

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Question

Suppose steel wires have the tensile strength represented by a normal distribution with mean value equal to 5000N and standard deviation equal to 150N. Knowing that these wires will be used in the manufacture of a steel cable to be mounted on the boom of a crane, what should be the number of wires to be used in the manufacture of this cable so that the probability of the cable breaking with a load less than 50,000N is 2%?
What would be the safety factor associated with this probability of failure?
Suppose the resistance of the cable is expressed by the sum of the resistance of the wires that make it up.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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