The Shear Strength of Each of Ten Test Spot Welds $\begin{array} { l l l l l l l l l l } 395 & 379 & 404 & 370 & 392 & 365 & 412 & 418 & 361 & 378\end{array}$

The shear strength of each of ten test spot welds is determined, yielding the following data (psi): $\begin{array} { l l l l l l l l l l } 395 & 379 & 404 & 370 & 392 & 365 & 412 & 418 & 361 & 378\end{array}$
a. Assuming that shear strength is normally distributed, estimate the true average shear strength and standard deviation of shear strength using the method of maximum likelihood.
b. Again assuming a normal distribution, estimate the strength value below which 95% of all welds will have their strengths. (Hint: What is the 95 percentile in terms of $\mu \text { and } \sigma$
? Now use the invariance principle.)