A $4\mathrm{.}59$m long $100\mathrm{.}0$ mm $-$by$-309\mathrm{.}9$mm$,$ solid rectangular cantilever wooden beam is carrying a uniformly distributed load $w($see Fig below$),$ with a mean load intensity of $w=2\mathrm{.}6k\frac{N}{m}$ and a COV of ${}_W=0\mathrm{.}15.$ The material is structural$-$grade redwood with a rated average yield strength $($parallel to grain under bending$)$ of ${}_y=28\mathrm{.}58\frac{N}{m}{m}^2$ and COV${}_y=0\mathrm{.}20.$ Assume log$-$normal distributions for $w$ and ${}_y.$ The resistance and load affect basic variables are independent.

Determine the probability $($expressed as a $\%$ to $1$ dp $)$ that the maximum extreme fibre stress in the beam will exceed the tensile yield strength of the wood.