Problem $2[10$ points$]$

A flexible pavement has a $4-$inch sand$-$mix asphalt wearing surface, $10-$inch soil$-$cement based, and a $10-$inch crushed stone subbase. It is designed to withstand $40020-$kip singleaxle loads and $90035-$kip tandem axle loads per day. The subgrade California Bearing Ratio $($CBR$)$ is $8,$ the overall standard deviation is $0\mathrm{.}45,$ the initial PSI is $4\mathrm{.}2,$ and the TSI is $2\mathrm{.}5.$ The drainage coefficients are $1\mathrm{.}0.$ What is the probability that this pavement will have a PSI above $2\mathrm{.}5$ after $25$ years?