A cable is made up of four wires. The breaking strength of each wire is a normally distributed random variable with mean 10 kN and standard deviation 1 kN. The strength of the cable, using the brittle wire method, is estimated to be the strength of the weakest wire multiplied by the number of wires.

Question

Emelia Burgess

Mathematics

4 August, 10:51

A cable is made up of four wires. The breaking strength of each wire is a normally distributed random variable with mean 10 kN and standard deviation 1 kN. The strength of the cable, using the brittle wire method, is estimated to be the strength of the weakest wire multiplied by the number of wires.

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Answers (1)

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Kash Buckley · Answer 1

a) μ = 35.858KN

b) median cable strength = 36.06KN

Step-by-step explanation:

Let X1, X2, X3, X4 represent the strength of the 4 wires.

We can find the median of the cable strength in minitab as:

Stat - Basic statistics - Display descriptive statistics-variable (C5) - statistics (median) - ok

Median cable strength is 36.06 KN

Therefore the estimate of the mean strength of the cable is 35.858 KN, and the estimate of the median cable strength is 36.06 KN.