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.
a. Use simulated samples of size 1000 to estimate the mean strength of this type of cable.
b. Estimate the median cable strength.
c. Estimate the standard deviation of the cable strength.
d. To be acceptable for a certain application, the probability that the cable breaks under a load of 28 kN must be less than 0.01. Does the cable appear to be acceptable? Explain.
(a) ? 36
(b) ? 36
(c) ? 2.8
(d) Yes, the cable is acceptable. The probability that the cable breaks under a load of 28 kN is approximately 0.005.
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