Probabilistic design using yield stress as the failure criterion must be accomplished...what minimum safety factor is acceptable?
Cumulative normal distribution is explained, e.g. on web page http://en.wikipedia.org/wiki/Normal_distribution
where mu is the center, sigma is the standard deviation, and x (z in your book) is the deviation from the center.
The value of Phi is the probability of the random quantity it describes to be less or equal ...
This provides an example of probabilistic design to determine minimum safety factor.