$6\mathrm{.}376\mathrm{.}38$A shaft is subjected to a maximum load of $20$ kN$.$ It is designed to withstand a load of $25$ kN$.$ If the maximum load encountered is normally distributed with a standard deviation of $3\mathrm{.}0$ kN$,$ and if shaft strength is normally distributed with a standard deviation of $2\mathrm{.}0$ kN$,$ what failure percentage would be expected?Assume that the failure rate calculated in Problem $6\mathrm{.}37$ is unacceptable.$($E$)$To what value would the standard deviation of shaft strength have to be reduced in order to give a failure rate of $5\%$h$,$ with no other changes?$($b$)$To what value would nominal shuft strength have to be increased in order to give a failure rate of only $5\%,$ with no other changes?