The strengths of individual bars made by a certain manufacturing process are approximately normally distributed with mean $105$MPa and standard deviation $8\mathrm{.}2$MPa. To ensure safety, a customer requires at least $95\%$ of the bars to be stronger than $95$MPa.

a$)$ Do the bars meet the requirement?

b$)$ By improved manufacturing techniques the manufacturer can make the bars more uniform. What value of the standard deviation will just meet the requirement if the mean stays the same?