Answer:
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