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.

Step 1 of 3:

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 is estimated to be the strength of the weakest wire multiplied by the number of wires.

To be applicable for a certain application, the probability that the cable break under a load of 28 KN must be less than 0.01.

Step 2 of 3:

We have to estimate the mean strength of the cable by using 1000 simulated samples.Let denote the strength of each wires, and Y denote the strength of the table.

Since it is given that the strength of the cable estimated as strength of the weakest wire multiplied with the number of wires.

We can generate the sample of size 1000 for by using the minitab software as

Calc- Random data- distribution- parameters(with sample size) - ok.

The generated samples will be different .

Find the product 4(min ( )).which will be the estimated cable strength of 1000 samples (store the variable in column C5).

We can estimate the mean strength of the cable using minitab as:

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

(which will be approximate values, it may change according to the sample)

(b) We have to find the estimate of median cable strength

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 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.