Problem $4(20\%)$

The Youngs modulus is measured with $10$ samples to be $E=18,000M$ and a standard deviation of $1,800M.$ The strain of the samples were measured to be $e=0\mathrm{.}007$ with an estimated standard uncertainty of $0\mathrm{.}000045.$ Estimate the stress of the samples and its uncertainty at $95\%$ of confidence level. Note that the Hooke's law indicates that the stress $S(M)$ equals the Young's modulus E times the strain e$,$ i$.$e$.,S=E^{**}e.$

Show your calculation procedure in the space.

Write your answers below:

$(1)(5\%)$ Relative uncertainty of the Youngs modulus$)$:

$(2)(5\%)$ Mean value of the stress $($Mpsi$)$:

$(3)(10\%)$ Uncertainty of the stress $($Mpsi$)$: