A steel cable consists of eight high-strength steel strands. The strength of each strand can be modeled by a lognormal random variable with a mean value of 50 kips and a coefficient of variation of 10%. What is the probability that the weakest strand will have a strength less than 40 kips?

P(X< 40) = 0.014367

Step-by-step explanation:

From the given information:

Suppose X denotes the strength of each steel strand & X follows the lognormal distribution with a mean value = 50 kips & coefficient of variation CV = 10%

Using the formula for the coefficient of variation CV

By applying the mean and mean & variance from the lognormal distribution, we have:

However, the next process is to replace the value of into the logman distributions mean.

3.912023 = μ +0.004975

μ = 3.907048

Now, we know our mean to be  3.907048 and the variance to be 0.00995.

Therefore, the probability that the weakest strand will have a strength of fewer than 40 kips can be computed as follows:

P(X< 40) = P(In(x) < In(40))

since;

P(X< 40) = P(Z < -2.18712)

Using the Excel formula =(=NORMDIST (-2.18712)

P(X< 40) = 0.014367

4.6875 pounds

step-by-step explanation: